POINTS ON CUBICS

A Search Page

If this is your first visit to the pages on Points on Cubics, you may wish to read the introductory page first. There, you will see that several classes of cubics are treated. Originally, selected cubics from all the classes comprised a single page of unwieldy size. The material was subdivided into a set of smaller pages, with the tables included.

However, some researchers need to be able to search a list consisting of all the cubics on one page. Therefore, this present page was produced by deleting material the original Points on Cubics.

For example, to find cubics passing through X(1113) and X(1114), type "1113, 1114" into the Find or Search tool on your browser.

Z(U,P): Pivotal Self-Isoconjugate Cubics
ZP(U,P): Z-Plus Cubics

H(U,P): Hirst Cubics
HP(U,P): H-Plus Cubics

C(U,L): Cross Conjugate Collinearity Cubics
ZC(U,L): ZC-Cubics

B(U,P): Bicentrics Collinearity Cubics
BP(U,P): B-Plus Cubics

D(U,P): Cross-Bicentrics Collinearity Cubics
DP(U,P): D-Plus Cubics


Z(U,P): Pivotal Self-Isoconjugate Cubics

upx(qy2 - rz2) + vqy(rz2 - px2) + wrz(px2 - qy2) = 0

Z(X(1),X(2)):
1, 6, 55, 57, 365, 1419, 2067, 4p2066, 6p1489, 9p2362, 57p2066, 364p365, 1419p2125

Z(X(1),X(3)):
1, 4, 1148

Z(X(1),X(4)):
1, 3, 90, 3p46

Z(X(1),X(6)):
1, 2, 87, 192, 366

Z(X(1),X(7)):
1, 6, 9, 55, 259, 6p236, 9p289, 9p1743, 523p1293

Z(X(1),X(8)):
1, 56, 84, 221, 266, 2067, 2362, 6p557, 6p558, 56p175, 56p176, 57p2066, 164p266, 225p1806, 266p505

Z(X(1),X(9)):
1, 57, 509, 1419

Z(X(1),X(10)):
1, 58, 267, 501

Z(X(1),X(11)):
1, 59, 100p266

Z(X(1),X(12)):
1, 21, 58, 60, 501, 21p266, 21p267, 21p1046, 21p2306, 21p2307, 58p1247, 284p554, 284p559

Z(X(1),X(21)):
1, 4, 65, 73, 1148

Z(X(1),X(27)):
1, 6, 55, 71, 72, 1214, 1751, 3p209, 72p1724, 1214p1754

Z(X(1),X(29)):
1, 3, 65, 73, 2067, 3p46, 10p2067, 12p1806, 46p921, 57p2066, 65p90, 485p2067

Z(X(1),X(31)):
1, 2, 75, 192, 330, 2p194

Z(X(1),X(33)):
1, 77, 2p2067, 7p2066, 77p1721

Z(X(1),X(34)):
1, 78, 2p2066, 8p2067, 78p1722

Z(X(1),X(37)):
1, 81, 2p2248, 58p1654

Z(X(1),X(55)):
1, 7, 174, 7p1742, 174p503

Z(X(1),X(56)):
1, 8, 188, 979, 8p978, 188p361

Z(X(1),X(57)):
1, 9, 9p509, 9p1743, 514p1293

Z(X(1),X(59)):
1, 11, 523, 9p1019, 11p1381, 11p1382, 174p650, 522p1381, 522p1382

Z(X(1),X(63)):
1, 19, 204, 2184

Z(X(1),X(65)):
1, 21, 1247, 2136, 21p1046, 21p2137

Z(X(1),X(75)) [ K175]:
1, 6, 19, 31, 48, 55, 56, 204, 221, 2192, 3p64, 64p1498, 207p268, 1034p2199

Z(X(1),X(76)):
1, 32, 6p365, 31p1631

Z(X(1),X(77)):
1, 33, 282, 2331

Z(X(1),X(78)):
1, 34, 207, 56p1034

Z(X(1),X(79)):
1, 35, 1129, 35p481, 35p482, 35p1127

Z(X(1),X(80)):
1, 15, 16, 36, 58, 106, 202, 203, 214, 501, 758, 1130, 13p36, 14p36, 36p484, 36p502, 36p1128, 38p202, 80p203

Z(X(1),X(81)):
1, 2, 37, 42, 192, 37p2162

Z(X(1),X(82)):
1, 38, 75, 1964, 2p194

Z(X(1),X(85)):
1, 41, 2067, 33p2066, 41p169, 41p508, 57p2066, 220p2362

Z(X(1),X(86)):
1, 6, 33, 37, 42, 55, 65, 73, 2331, 3p1903, 20p2357, 40p64, 64p1490

Z(X(1),X(88)):
1, 44, 88, 678, 13p1250

Z(X(1),X(92)):
1, 31, 48, 63, 2066, 2067, 2p184, 3p193, 3p371, 3p372, 6p485, 6p486, 9p2067, 57p2066, 371p493, 372p494

Z(X(1),X(98)):
1, 511, 511p1756

Z(X(1),X(99)):
1, 512, 1015, 1018

Z(X(1),X(100)):
1, 100, 244, 513, 100p1054

Z(X(1),X(101)):
1, 514, 190p2350, 1086p1621

Z(X(1),X(104)):
1, 80, 517, 3p1845

Z(X(1),X(105)):
1, 291, 518, 238p518, 291p2108

Z(X(1),X(107)):
1, 520, 40p1364, 282p1020

Z(X(1),X(158)):
1, 3, 255, 921, 1069, 1124, 1335, 3p46, 3p155, 3p371, 3p372, 3p485, 3p486, 3p487, 3p488, 6p493, 6p494

Z(X(1),X(226)):
1, 21, 31, 48, 1172, 2194, 21p1046, 31p1247, 1762p2194

Z(X(1),X(273)):
1, 3, 6, 55, 212, 219, 3p46, 9p2164, 21p2174, 55p224, 71p79, 71p1780

Z(X(1),X(279)):
1, 8, 9, 37, 42, 210, 8p978, 9p1743, 42p979, 523p1293

Z(X(1),X(310)):
1, 6, 55, 213, 1402, 1918, 1402p1764

Z(X(1),X(313)):
1, 31, 48, 58, 501, 1474, 2206, 31p267

Z(X(1),X(321)):
1, 28, 31, 48, 81, 1333, 6p2248, 58p199, 58p1654

Z(X(1),X(326)):
1, 19, 33, 34, 204, 207, 1096, 2331, 4p64, 4p1033, 4p1436, 25p1032, 25p1034

Z(X(1),X(346)):
1, 56, 57, 221, 1407, 1419, 1422, 56p366

Z(X(1),X(561)):
1, 31, 48, 560, 1973, 2156, 6p206, 6p1676, 6p1677, 25p159, 32p1670, 32p1671

Z(X(1),X(673)):
1, 6, 55, 241, 292, 518, 672, 673, 55p1362, 238p518, 291p2110

Z(X(1),X(739)):
1, 2, 192, 536, 899, 10p715, 75p739, 87p899, 899p899

Z(X(1),X(903)):
1, 6, 44, 55, 106, 678, 902, 1319, 2161, 2342, 3p1846, 6p214

Z(X(1),X(961)):
1, 8, 21, 960, 1193, 2292, 8p978, 21p1046, 43p256, 256p846, 979p1193, 1247p2292, 1999p2269

Z(X(1),X(1043)):
1, 34, 56, 64, 65, 73, 207, 221, 1042, 7p2357, 20p1042, 1034p1410

Z(X(1),X(1219)):
1, 56, 221, 1191, 1697, 2334, 84p1697

Z(X(1),X(1220)):
1, 58, 501, 1193, 2067, 2292, 57p2066, 267p2292, 429p1805, 429p1806, 501p2127

Z(X(1),X(1259)):
1, 4, 34, 207, 1118, 1148, 4p266, 34p1034

Z(X(1),X(1268)):
1, 6, 55, 58, 501, 1100, 1962, 2160, 2308, 6p553, 35p1100, 267p1962

Z(X(1),X(1804)):
1, 4, 33, 1148, 1857, 2331, 4p259, 4p282

Z(X(1),X(1821)):
1, 31, 48, 240, 1755, 1821, 1959, 1967, 3p1987, 6p2009, 6p2010, 55p1355, 232p401, 325p1691, 511p1687, 511p1688

Z(X(1),X(1911)):
1, 2, 86, 192, 239, 257, 335, 350, 385, 740, 2p294, 2p2068, 2p2069, 75p727, 81p1655, 87p239, 238p239, 238p726, 239p241, 274p2107, 740p2106, 1281p2113, 1654p1929

Z(X(1),X(1927)):
1, 75, 336, 350, 1909, 1926, 1934, 1934, 1966, 2p83, 2p194, 2p732, 43p1909, 76p695, 76p699, 87p350, 240p1966, 384p385, 385p385, 385p698

Z(X(1),X(1934)):
1, 31, 48, 82, 172, 1428, 1580, 1910, 1914, 1927, 1933, 2330, 4p1691, 31p1281, 31p2236, 32p695, 147p1976, 194p699, 237p385, 384p385, 385p385, 385p2076

Z(X(1),X(2221)):
1, 2, 192, 612, 1219, 2345, 87p612, 1191p2345

Z(X(1),X(2287)):
1, 57, 65, 73, 278, 1419, 1427

Z(X(2),X(1)) [Thomson cubic, K002]:
1, 2, 3, 4, 6, 9, 57, 223, 282, 1073, 1249, 84p1490, 204p1032, 221p1034, 1073p1712

Z(X(2),X(2)):
2, 31, 365, 6p1631, 365p510

Z(X(2),X(3)):
2, 19, 19p1763

Z(X(2),X(4)):
2, 48, 48p1726

Z(X(2),X(5)):
2, 2148

Z(X(2),X(6)):
1, 2, 7, 9, 366, 1489, 2p1419, 2p2067, 7p2066, 8p2362, 92p2066, 173p1489, 364p366

Z(X(2),X(7)):
2, 41, 259, 55p1626, 259p362

Z(X(2),X(8)):
2, 266, 604, 266p504

Z(X(2),X(9)):
2, 56, 478, 509, 2362, 2p2067, 7p2066, 225p1806

Z(X(2),X(10)):
2, 3, 6, 28, 81, 1333, 2p501, 6p267

Z(X(2),X(19)):
2, 3, 6, 69, 485, 486, 2p2066, 2p2067, 7p2066, 8p2067, 48p491, 48p492

Z(X(2),X(29)):
2, 63, 1400, 1409, 45p63, 65p2164, 1400p1764

Z(X(2),X(32)):
2, 75, 330, 2p192, 2p366

Z(X(2),X(33)):
2, 57, 63, 222, 223, 2p1433, 46p63, 222p1158, 912p2006

Z(X(2),X(34)):
1, 2, 9, 63, 78, 219, 8p2164, 9p224, 12p1789, 21p35, 46p63, 72p1780

Z(X(2),X(37)):
2, 3, 6, 27, 58, 86, 2248, 58p1761, 81p1654

Z(X(2),X(55)):
2, 57, 174, 189, 223, 557, 558, 1659, 2p2067, 7p2066, 57p175, 57p176, 164p174, 174p505, 273p2066

Z(X(2),X(56)):
1, 2, 8, 9, 188, 236, 8p289, 8p1743, 514p1293

Z(X(2),X(57)):
2, 55, 2p2067, 7p2066, 9p509, 9p1486, 200p2362, 281p2066

Z(X(2),X(58)):
1, 2, 9, 10, 37, 226, 281, 1214, 2p2331, 10p1433, 20p1903, 40p2184, 1490p2184

Z(X(2),X(59)):
2, 2170, 174p650, 513p1222, 514p2347

Z(X(2),X(64)):
2, 57, 223, 3p1249, 8p610, 20p282

Z(X(2),X(65)):
2, 3, 6, 29, 284, 333, 6p1247, 284p1762, 314p2305

Z(X(2),X(73)):
2, 4, 21, 1172, 1249, 9p229, 21p2184

Z(X(2),X(75)) [ K177]:
2, 3, 6, 25, 32, 66, 206, 1676, 1677, 19p159, 31p1670, 31p1671

Z(X(2),X(82)):
2, 3, 6, 39, 141, 427, 38p1342, 38p1343, 63p66, 427p2172, 1370p2156

Z(X(2),X(86)):
1, 2, 9, 42, 213, 1400, 1400p1764

Z(X(2),X(87)):
1, 2, 9, 43, 1423, 2176, 37p904

Z(X(2),X(91)):
2, 3, 6, 24, 70, 571, 1993, 26p47, 49p2190, 161p1748

Z(X(2),X(92)):
2, 184, 31p485, 31p486, 31p1670, 31p1671, 48p157, 48p491, 48p492, 63p1676, 63p1677, 75p1485

Z(X(2),X(99)):
2, 798, 10p932, 192p1977

Z(X(2),X(100)):
2, 649, 100p596, 244p595

Z(X(2),X(101)):
2, 513, 668, 1015, 1978p1979

Z(X(2),X(103)):
2, 57, 105, 223, 910, 8p910, 271p1886, 516p518

Z(X(2),X(106)):
1, 2, 9, 44, 80, 88, 214, 519, 2p678, 2p1319, 2p2342, 57p1145

Z(X(2),X(109)):
2, 11, 100, 650, 101p149

Z(X(2),X(110)):
2, 244, 661, 2p1018

Z(X(3),X(1)) [McCay cubic, K003]]:
1, 3, 4, 1075, 1745

Z(X(3),X(2)):
3, 19, 55, 57, 84, 198, 365

Z(X(3),X(7)):
1, 3, 33, 55, 198, 259, 282, 1745

Z(X(3),X(8)):
1, 3, 34, 56, 266, 1035, 1745, 56p1034

Z(X(3),X(75)) [ K172]:
3, 6, 25, 55, 56, 64, 154, 198, 1033, 1035, 1436, 31p1032, 31p1034

Z(X(4),X(1)) [Orthocubic, K006] :
1, 3, 4, 46, 90, 155, 254, 371, 372, 485, 486, 487, 488, 3p1123, 3p1336, 19p493, 19p494

Z(X(4),X(31)) [ K170]:
2, 4, 69, 193, 487, 488, 2p2128, 2p2129, 19p1267, 63p1123, 91p1599, 91p1600, 92p493, 92p494

Z(X(4),X(63)):
2, 4, 6, 25, 193, 371, 372, 2362, 4p2066, 9p2362, 19p485, 19p486, 193p2129, 225p1806

Z(X(4),X(75)) [ K176]:
3, 4, 6, 25, 155, 184, 571, 2165, 25p921

Z(X(4),X(77)):
1, 4, 9, 19, 33, 46, 55, 9p1723, 10p2160, 29p2174, 33p90, 37p1780

Z(X(4),X(78)):
1,4,34,46, 56, 84, 208, 34p90, 36p915, 56p1158, 80p1455, 84p1720, 102p1870, 1411p1737

Z(X(5),X(1)) [Feuerbach cubic, K005]:
1, 3, 4, 5, 17, 18, 54, 61, 62, 195, 627, 628, 2120, 2121, 74p1749

Z(X(6),X(1)) [Grebe cubic, K102] :
1, 2, 6, 43, 87, 194

Z(X(6),X(6)):
6, 75, 366

Z(X(6),X(57)):
1, 6, 8, 9, 43, 979, 2319, 9p509, 9p978, 10p893, 21p171, 284p1999, 846p1247

Z(X(7),X(1)):
1, 7, 9, 55, 57, 218, 277

Z(X(6),X(33)):
1, 3, 7, 57, 63, 77, 90, 224, 3p1708, 21p2003, 46p77, 79p1214

Z(X(7),X(55)):
1, 2, 7, 57, 145, 174, 1488, 2089, 145p2137

Z(X(8),X(1)):
1, 8, 40, 56, 84, 2122, 2123

Z(X(8),X(6)):
1, 2, 8, 40, 57, 144, 189, 366

Z(X(8),X(31)):
2, 7, 8, 144, 175, 176, 1143, 1274, 2p364, 2p2124, 2p2125, 19p1267, 63p1123

Z(X(8),X(34)):
1, 3, 8, 40, 78, 90, 271, 3p1158, 10p1800, 80p912, 271p1720, 515p1807

Z(X(8),X(56)) [ K199] :
1, 8, 40, 175, 176, 188, 280, 483, 2p2066, 8p2067, 8p2362, 9p557, 92p2066, 164p188, 188p505

Z(X(8),X(58)) [Spieker central cubic, K033] :
1, 4, 8, 10, 40, 65, 72, 2p1903, 4p1490, 8p64, 10p1394, 73p1034, 1032p2331

Z(X(8),X(106)):
1, 8, 40, 104, 519, 1145, 1319, 1339, 44p189

Z(X(9),X(1)):
1, 9, 57, 165, 364, 2124, 2125, 3p1123, 6p175, 6p176, 6p1143, 6p1274

Z(X(9),X(2)):
1, 6, 9, 56, 84, 165, 198, 365, 34p271

Z(X(9),X(81)):
1, 4, 9, 37, 65, 71, 165

Z(X(9),X(86)):
6, 9, 19, 37, 71, 198, 1400, 1903, 8p2155, 9p207, 20p1400, 1034p1409, 1498p1903

Z(X(9),X(105)):
1, 2, 9, 105, 165, 241, 518, 672, 2p103, 2p1742, 8p1362, 43p291, 59p1566, 291p1282, 518p1376, 1280p1743

Z(X(10),X(1)):
1, 10, 58, 191, 267, 2126, 2127, 3p1123, 3p1336

Z(X(10),X(6)):
1, 2, 10, 81, 191, 366, 1029, 1654, 2p2248, 1255p1961

Z(X(10),X(56)):
1, 8, 10, 21, 188, 191, 1247, 2p1250, 2p1251, 8p267, 8p1046, 9p554, 9p559, 484p1320

Z(X(10),X(81)):
2, 4, 6, 10, 42, 71, 199, 1654, 37p2248

Z(X(13),X(1)):
1, 13, 15, 18, 62, 13p202

Z(X(14),X(1)):
1, 14, 16, 17, 61, 14p203

Z(X(19),X(1)):
1, 19, 63, 1707, 2128, 2129, 3p1123, 3p1336, 4p493, 4p494, 6p487, 6p488, 371p486, 372p485

Z(X(19),X(19)):
19, 326, 2p493, 2p494, 6p487, 6p488

Z(X(20),X(1)) [Darboux cubic, K004]:
1, 3, 4, 20, 40, 64, 84, 1490, 1498, 2130, 2131, 19p1032, 56p1034

Z(X(20),X(6)):
20, 40, 189, 366, 1490, 2184, 57p1034

Z(X(20),X(75)):
3, 6, 20, 25, 393, 577, 1498, 1661, 6p2155, 1032p1973, 1973p2063

Z(X(21),X(10)):
1, 3, 21, 28, 56, 58, 84, 1394, 2360, 21p64, 21p207, 84p1498, 603p1034

Z(X(21),X(75)):
1, 3, 6, 21, 25, 31, 37, 1333, 1402, 2217, 6p573, 31p1764, 37p572, 58p197, 1400p1610

Z(X(23),X(75)) [ K108]:
3, 6, 23, 25, 111, 187, 1177, 6p2157, 31p858

Z(X(27),X(1)) [ K109]:
1, 3, 4, 19, 27, 63, 71, 226, 284, 579, 1751, 1780, 3p1713, 63p1714, 72p1612, 226p580, 377p2219

Z(X(27),X(71)):
1, 2, 7, 27, 28, 579, 1172, 2p1724, 4p272, 7p1754

Z(X(28),X(63)):
1, 2, 19, 25, 28, 37, 1724, 469p1245, 2214p2303

Z(X(28),X(75)):
3, 6, 19, 25, 28, 48, 65, 228, 2194, 2218, 2352, 3p1714, 6p1780, 48p1713, 65p580, 71p1612

Z(X(30),X(1)) [Neuberg cubic, K001]:
1, 3, 4, 13, 14, 15, 16, 30, 74, 399, 484, 617, 1138, 1157, 1263, 1276, 1277, 1337, 1338, 2132, 2133

Z(X(30),X(75)):
3, 6, 25, 30, 50, 399, 1989, 6p2159, 31p146, 31p1138, 31p2071

Z(X(35),X(2)):
35, 55, 57, 267, 365, 1030, 2160

Z(X(35),X(75)):
6, 35, 42, 55, 56, 58, 1030, 6p267, 6p2160

Z(X(36),X(75)):
6, 36, 55, 56, 106, 902, 909, 2183, 6p2161

Z(X(37),X(2)):
1, 6, 37, 58, 267, 365, 846, 1030, 2248, 1126p1961

Z(X(37),X(7)):
6, 9, 37, 259, 284, 1030, 1250, 1251, 6p1247, 8p2305, 9p267, 35p1251, 55p554, 484p2316

Z(X(37),X(57)):
1, 9, 21, 37, 846, 893, 1247, 2p2329, 8p2248, 8p2305, 9p509, 9p1999, 43p979, 978p2319

Z(X(40),X(2)):
40, 55, 57, 365, 1436, 2066, 2362, 6p1490, 9p2067, 56p1034, 225p1806

Z(X(40),X(75)) [ K179]:
6, 34, 40, 55, 56, 212, 2208, 6p1490, 212p1767, 604p1034

Z(X(40),X(86)):
19, 40, 55, 64, 65, 71, 2357, 6p1490, 10p154, 65p1498, 607p1032, 1034p1400

Z(X(42),X(6)):
1, 2, 42, 274, 366, 1045

Z(X(56),X(2)):
9, 55, 56, 57, 365, 1423, 2053, 2137, 6p2136

Z(X(56),X(9)):
1, 2, 56, 57, 87, 509, 978, 1423, 10p1431, 57p979, 58p894, 58p1999

Z(X(57),X(1)):
1, 9, 57, 173, 258, 1743, 2136, 2137, 514p1293

Z(X(57),X(6)):
7, 8, 9, 57, 366, 2136, 2319, 2p1423, 2p2137

Z(X(57),X(8)):
1, 6, 56, 57, 266, 289, 1743, 6p2089, 1743p2137

Z(X(57),X(21)):
1, 2, 37, 57, 65, 1400, 1743, 2p978, 979p1400

Z(X(57),X(80)):
1, 36, 57, 284, 1743, 1795, 1845, 2316, 2323, 2p1464, 44p1443, 102p223, 173p1130, 258p1130

Z(X(57),X(86)):
9, 55, 57, 65, 1334, 1400, 2136, 42p2137

Z(X(63),X(1)):
1, 9, 19, 40, 57, 63, 84, 610, 1712, 2184, 2p1035, 6p1032, 6p1034

Z(X(63),X(6)):
4, 7, 9, 40, 63, 189, 366

Z(X(63),X(56)):
2, 9, 40, 63, 188, 280, 281, 2p1745, 164p236

Z(X(63),X(75)):
1, 6, 31, 63, 220, 610, 1407, 1973, 2155, 6p159, 6p1763, 6p2138, 6p2139, 1801p1824

Z(X(65),X(8)):
1, 56, 58, 65, 266, 267, 1046, 2306, 2307, 6p554, 6p559, 56p191, 56p1247, 106p484

Z(X(65),X(9)):
1, 57, 65, 81, 509, 894, 1046, 1431, 1999, 2p2248, 56p1654, 57p1247, 87p978, 979p1423

Z(X(65),X(31)):
2, 7, 8, 65, 257, 314, 894, 1999, 7p1045

Z(X(65),X(75)):
6, 55, 56, 65, 2160, 2174, 2194, 6p1781, 41p1029, 56p191, 1717p2164, 1723p2164

Z(X(69),X(1)) [ K169]:
1, 2, 6, 20, 25, 64, 69, 159, 200, 269, 1763, 2138, 2139, 1801p1826

Z(X(69),X(31)) [Lucas cubic, K007] :
2, 4, 7, 8, 20, 69, 189, 253, 329, 1032, 1034, 2p1712, 7p1490

Z(X(69),X(75)) [ K178]:
6, 69, 159, 1974

Z(X(69),X(82)) [ K140]:
6, 66, 69, 141, 159, 1843, 22p38

Z(X(75),X(6)):
6, 75, 366, 1631, 366p510

Z(X(75),X(31)) [Spieker perspector cubic, K034] :
1, 2, 7, 8, 63, 75, 92, 280, 347, 1895, 2p1073, 189p1490, 223p1034, 253p1498, 1032p1249

Z(X(75),X(42)):
1, 27, 58, 63, 75, 86, 267, 75p501

Z(X(75),X(75)):
6, 75, 560, 1631, 6p1670, 6p1671, 6p1676, 6p1677, 75p1672, 75p1673

Z(X(76),X(1)):
1, 32, 76, 1670, 1671, 1676, 1677, 1759, 76p1672, 76p1673

Z(X(76),X(31)) [ K141]:
2, 4, 6, 22, 69, 76, 1670, 1671, 19p1370, 66p75, 75p1676, 75p1677

Z(X(77),X(55)):
1, 4, 7, 77, 174, 189, 223, 7p1745, 164p2089, 505p1488

Z(X(78),X(6)):
1, 2, 78, 278, 366, 1490, 57p1034

Z(X(78),X(56)):
1, 4, 8, 78, 188, 1034, 1490, 8p1745

Z(X(80),X(36)):
1, 10, 13, 14, 80, 484, 502, 519, 759, 1128, 1168, 13p35, 14p35, 80p202, 80p203, 80p501, 80p1130

Z(X(81),X(10)):
1, 6, 57, 58, 81, 222, 284, 1172, 1433, 4p2360, 20p1436, 64p1817

Z(X(83),X(38)):
2, 4, 6, 83, 251, 1176, 1342, 1343, 4p2172, 1799p2156

Z(X(84),X(6)):
40, 189, 329, 366, 6p189, 40p87, 43p189

Z(X(84),X(75)) [ K180]:
6, 33, 84, 198, 221, 603, 963, 1436, 2187, 2192, 6p2270, 198p1622, 603p1753

Z(X(86),X(42)):
1, 2, 7, 21, 29, 77, 81, 86, 2p1433, 4p1817, 20p84, 253p2360, 1034p1394

Z(X(87),X(2)):
43, 87, 365, 1423, 2053, 2162, 2176

Z(X(92),X(1)):
1, 19, 47, 48, 63, 91, 92, 2p155, 6p254

Z(X(96),X(75)):
5, 6, 24, 96, 571, 2165, 2351, 5p2158, 6p2148, 6p2180, 26p2148

Z(X(98),X(1)):
1, 98, 511, 1687, 1688, 1756, 2009, 2010, 98p2007, 98p2008

Z(X(99),X(1)) [Steiner cubic, K035] :
1, 39, 83, 99, 512, 1018, 1019, 1379, 1380, 1379p1577, 1380p1577

Z(X(100),X(6)):
100, 142, 366, 514, 2346, 2p1381, 2p1382, 522p1381, 522p1382

Z(X(101),X(2)):
101, 354, 365, 513, 1174, 1381, 1382, 650p1381, 650p1382

Z(X(108),X(78)):
4, 56, 108, 513, 1381, 1382, 65p1113, 65p1114, 513p1113, 513p1114

Z(X(109),X(8)):
58, 65, 109, 266, 513, 1381, 1382, 513p1381, 513p1382

Z(X(110),X(1)):
1, 5, 54, 110, 523, 1113, 1114, 9p1019, 9p1020, 523p1822, p23p1823

Z(X(165),X(75)):
6,55,56, 165, 269, 1253, 1615, 56p2125

Z(X(171),X(1)):
1, 10, 43, 58, 87, 171, 256, 846, 2p2248, 978p1247, 979p1046

Z(X(171),X(2)) [ K131]:
2, 31, 42, 43, 55, 57, 81, 171, 365, 846, 893, 2162, 2248, 6p1045, 1282p2111

Z(X(171),X(75)):
6, 55, 56, 86, 171, 904, 1918, 6p1045

Z(X(172),X(75)):
6, 37, 172, 893, 1333, 2162, 2176, 2248, 6p846, 979p2305

Z(X(172),X(76)):
1, 32, 41, 56, 58, 172, 213, 904, 2176, 6p365, 6p846, 6p2162, 6p2248, 31p1045, 727p1757, 1189p1972

Z(X(174),X(1)):
1, 173, 174, 188, 258, 259, 266, 145p259

Z(X(189),X(1)):
1, 40, 84, 189, 198, 222, 223, 281, 282, 2270, 2p963, 40p1622, 222p1753

Z(X(190),X(106)):
88, 100, 190, 644, 900, 1120, 1635, 2p678, 7p1635, 519p1149

Z(X(220),X(2)):
1, 6, 170, 220, 269, 365, 1615, 57p2125

Z(X(220),X(7)):
6, 9, 57, 220, 259, 1615, 9p1742, 259p844

Z(X(222),X(8)):
6, 19, 57, 84, 221, 222, 266, 57p1745, 289p505

Z(X(226),X(1)):
1, 9, 35, 57, 79, 226, 284, 1781, 7p1030, 9p267, 90p1717, 90p1723

Z(X(226),X(29)):
1, 48, 63, 73, 226, 1400, 1781

Z(X(226),X(41)):
2, 7, 86, 226, 508, 1432, 1909, 2p1046, 2p1999, 7p846, 7p1247, 75p2248, 330p978

Z(X(226),X(55)) [ K134]:
2, 57, 81, 174, 226, 554, 559, 1029, 1081, 1082, 2p1046, 7p1030, 57p1247, 88p484

Z(X(237),X(75)):
3, 6, 25, 98, 237, 694, 1691, 1971

Z(X(238),X(1)):
1, 238, 291, 2108, 2p2109

Z(X(238),X(2)) (2nd equal areas cubic, [ K155]):
1, 2, 6, 31, 105, 238, 292, 365, 672, 1423, 1931, 2053, 2054, 2106, 2107, 2108, 2109, 2110, 2111, 2112, 2113, 2114, 2115, 2116, 2117, 2118, 2119, 2144, 2145, 2146, 2147, 2p727, 6p1575, 1045p2248, 1281p1967

Z(X(238),X(7)):
6, 9, 238, 259, 2110, 8p1911, 9p2111

Z(X(238),X(9)):
87, 238, 509, 1423, 2114, 7p292, 7p2115

Z(X(238),X(27)):
6, 72, 238, 2110, 10p2196, 72p2111

Z(X(238),X(57)):
1, 9, 238, 2108, 8p292, 8p2109, 9p509

Z(X(238),X(239)):
238, 672, 6p1575, 105p291, 291p292, 335p727

Z(X(239),X(6)):
1, 2, 6, 75, 239, 291, 366, 518, 673, 1575, 2319, 2p1423, 2p1931, 2p2054, 2p2106, 2p2107, 2p2108, 2p2109, 2p2110, 2p2111, 2p2112, 2p2112, 2p2113, 2p2114, 2p2115, 2p2116, 2p2117, 2p2118, 2p2119, 2p2144, 2p2145, 2p2146, 2p2147, 75p727, 694p1281, 1655p2248

Z(X(240),X(63)):
1, 19, 63, 240, 1096, 1910, 1967, 2312, 2p419, 2p1692, 4p401, 4p1297, 25p147, 64p193, 297p2065

Z(X(241),X(2)):
55, 57, 241, 365, 2114, 2115, 2195

Z(X(241),X(9)):
1, 9, 57, 105, 241, 269, 292, 509, 910, 1279, 1447, 2114, 2p1477, 7p103, 7p2115, 87p1742, 355p1355, 1425p1427

Z(X(241),X(75)):
6, 55, 56, 220, 241, 910, 911, 1279, 1407, 3p2191, 6p2195, 19p218, 25p1810

Z(X(243),X(3)):
1, 3, 4, 158, 243, 415, 1937, 4p416, 90p1148, 1047p1247

Z(X(253),X(1)):
1, 20, 64, 154, 253, 1073, 1249, 7p221, 8p2192

Z(X(264),X(31)) [Euler perspector cubic, K045] :
2, 3, 4, 69, 254, 264, 1993, 2p91, 69p920

Z(X(265),X(1)):
5, 30, 54, 74, 186, 265, 35p80, 36p79, 79p1458

Z(X(278),X(78)):
1, 6, 19, 34, 57, 278, 1723, 2p1406, 4p2164, 6p1708, 27p2174, 65p79, 267p1717, 267p1781, 1570p1987, 1770p2160

Z(X(385),X(1)) [ K128]:
1, 2, 6, 32, 76, 98, 385, 511, 694, 1423, 2319, 4p1740, 6p2227, 19p147, 75p699, 292p1281

Z(X(286),X(31)):
2, 4, 21, 63, 69, 72, 92, 286, 1441, 2p579, 2p1751, 2p1780, 63p1713, 69p1714, 306p1612, 580p1441

Z(X(291),X(2)):
42, 81, 105, 291, 365, 672, 1914

Z(X(291),X(239)) [ K135]:
1, 6, 42, 57, 239, 291, 292, 672, 894, 1757, 1967, 2p741, 8p1911, 37p2248, 105p291, 238p2113, 241p2115, 291p1911, 292p1929, 741p1654, 1281p1911, 1463p2053, 1575p2109

Z(X(292),X(238)) [ K136]:
1, 2, 37, 87, 171, 238, 241, 291, 292, 1575, 1581, 2p741, 37p2106, 43p291, 291p291, 291p294, 291p2068, 291p2069, 335p727, 518p2111, 741p1655

Z(X(297),X(48)):
2, 4, 69, 98, 230, 297, 393, 694, 1503, 4p1966, 19p147, 92p401, 92p1297, 193p2184

Z(X(297),X(75)):
3, 6, 25, 230, 297, 394, 1503, 2207, 31p248, 31p1297, 47p66, 91p206, 1755p2065

Z(X(304),X(31)):
1, 2, 19, 75, 279, 304, 346, 2184, 2p20, 2p159, 2p1763, 2p2138, 2p2139

Z(X(309),X(31)) [ K133]:
2, 40, 77, 189, 280, 309, 318, 329, 347, 962, 75p963, 77p1753, 329p1622

Z(X(314),X(31)):
1, 2, 4, 65, 69, 75, 81, 314, 321, 1764, 2p573, 75p2217, 81p1766, 226p1610, 321p572

Z(X(316),X(31)) [Droussent cubic, K008] :
2, 4, 67, 69, 316, 524, 671, 858, 75p1177

Z(X(319),X(31)):
2, 7, 8, 10, 79, 86, 319, 1029, 2p191

Z(X(320),X(31)):
2, 7, 8, 80, 320, 519, 903, 908, 2p104

Z(X(322),X(31)) [ K154]:
2, 7, 8, 78, 84, 273, 322, 2p1490, 57p1034, 57p2057

Z(X(333),X(1)):
1, 2, 6, 10, 19, 58, 63, 333, 573, 1400, 2p2217, 6p1764, 10p572, 21p478, 65p1610

Z(X(356),X(1)) [a Morley cubic, K029] :
1, 356, 357, 358, 1134, 1137, 1507, 1508

Z(X(365),X(1)) [a Morley cubic, K029]:
1, 365, 366, 43p366, 87p365

Z(X(366),X(1)) [a Morley cubic, K029]:
1, 364, 365, 366, 7p365, 9p365, 365p1489, 366p1419, 366p2067

Z(X(384),X(1)) [a Brocard cubic, K020] :
1, 3, 4, 32, 39, 76, 83, 194, 384, 695, 31p1031

Z(X(393),X(63)) [ K163]:
3, 4, 6, 254, 393, 459, 1609

Z(X(395),X(1)) [ K129a]:
1, 2, 6, 14, 16, 18, 62, 395, 1653, 19p617, 19p628, 621p2159, 622p2148

Z(X(396),X(1)) [ K129b]:
1, 2, 6, 13, 15, 17, 61, 396, 1652, 19p627, 621p2148, 622p2159

Z(X(476),X(1)) [ K130] :
1, 30, 74, 110, 476, 523, 626, 110p1749, 1109p1291

Z(X(511),X(31)):
2, 4, 69, 290, 385, 401, 511, 1916, 1972

Z(X(511),X(92)):
3, 6, 25, 248, 385, 394, 401, 511, 1297, 3p1967, 3p2312, 31p147, 48p230, 48p1987, 1073p1707, 1959p2065

Z(X(512),X(1)) [1st Equal Areas Cubic, K021] :
1, 99, 512, 2142, 2143

Z(X(515),X(1)):
1, 36, 40, 80, 84, 102, 515, 90p1718, 90p1720

Z(X(515),X(86)):
33, 40, 48, 73, 515, 1826, 2183, 2250, 2357, 42p102, 65p1295, 1528p2188

Z(X(517),X(7)):
1, 19, 44, 55, 102, 219, 259, 517, 2316, 2342, 9p2182, 145p2192

Z(X(518),X(57)):
1, 9, 57, 200, 239, 294, 518, 1280, 1282, 2348, 2p103, 2p2115, 8p1911, 9p509, 9p910, 1742p2319

Z(X(894),X(1)):
1, 9, 57, 213, 274, 893, 894, 1045

Z(X(894),X(6)) [ K132]:
6, 7, 9, 37, 75, 86, 87, 192, 256, 366, 894, 1045, 1654, 2p2248, 1575p1929

Z(X(894),X(31)):
2, 81, 192, 257, 321, 330, 894, 1654, 75p2248

Z(X(1465),X(8)):
3, 6, 34, 57, 106, 266, 909, 1319, 1465, 2182, 57p102, 84p1743, 164p289

Z(X(1580),X(75)) ( = H(X(31),X(1)) ):
1, 6, 31, 75, 560, 1403, 1580, 1755, 1910, 1967, 2053, 2p699, 4p1613, 25p147, 31p2227, 83p2076, 1281p1911

Z(X(1770),X(1)):
1, 35, 46, 79, 90, 191, 267, 1717, 1770, 1780

Z(X(1909),X(32)):
1, 8, 10, 76, 85, 257, 274, 330, 1655, 1909, 2p192, 2p366, 2p1654, 75p2248, 726p1919

Z(X(1914),X(76)):
1, 6, 31, 32, 727, 1326, 1403, 1438, 1911, 1914, 2223, 6p365, 6p2053, 6p2054, 6p2106, 6p2107, 6p2108, 6p2109, 6p2110, 6p2111, 6p2112, 6p2113, 6p2114, 6p2115, 6p2116, 6p2117, 6p2118, 6p2119, 6p2144, 6p2145, 6p2146, 6p2147, 31p1575

Z(X(1935),X(9)):
34, 58, 63, 87, 226, 509, 1046, 1423, 1745, 1935, 57p1247

Z(X(1966),X(31)) ( = H(X(75),X(1)) ):
1, 2, 31, 75, 561, 1581, 1821, 1959, 1966, 2227, 2p1423, 2p2319, 4p147, 4p194, 76p699, 291p1281, 308p2076

Z(X(2328),X(75)):
1, 6, 31, 64, 71, 154, 1042, 1474, 2128

Z(X(2360),X(75)):
6, 19, 48, 64, 73, 154, 2299, 2357, 2360


ZP(U,P): Z-Plus Cubics

upx(qy2 + rz2) + vqy(rz2 + px2) + wrz(px2 + qy2) = 0

ZP(X(1),X(244)):
100, 813, 1023, 1025, 2p901, 6p874, 8p919, 100p1931, 101p447, 190p2054, 545p901

ZP(X(2),X(292)):
1, 190, 239, 659, 2p1023, 88p659

ZP(X(3),X(651)):
1, 6, 522, 650, 8p2183, 104p513, 523p1822, 523p1823, 650p1113, 65pp1114

ZP(X(3),X(662)):
6, 325, 523, 19p878, 523p1822, 523p1823, 6661p1113, 661p1114

ZP(X(4),X(296)):
1, 243, 653, 108p527, 243p652

ZP(X(5),X(655)):
1, 523. 654. 36p294

ZP(X(6),X(244)):
100, 660, 898, 31p874, 100p899, 100p2107, 190p2106, 422p1331, 537p901

ZP(X(6),X(291)):
1, 100, 238, 659, 100p899, 739p812

ZP(X(6),X(658)):
55, 241, 650, 200p884, 650p1381, 650p1382

ZP(X(9),X(11)):
100, 109, 677, 59p676, 100p1155, 109p1156, 144p1461

ZP(X(9),X(101)):
1, 514, 1027, 2p518, 514p1381, 514p1382, 522p1381, 522p1382

ZP(X(9),X(105)):
1, 100, 518, 2254, 88p1642, 100p1155, 518p1381, 518p1382, 519p840, 522p1381, 522p1382, 665p1121

ZP(X(9),X(106)):
1, 519, 1026, 105p900, 519p1381, 519p1382, 522p1381, 522p1382

ZP(X(19),X(293)):
1, 162, 240, 4p684, 30p842, 110p468, 240p1822, 240p1823, 523p1113, 523p1114, 691p868

ZP(X(21),X(662)):
1, 6, 523, 661, 10p2245, 513p759, 523p1379, 523p1380, 523p1822, 523p1823, 661p1113, 661,1114

ZP(X(25),X(336)):
6, 112, 232, 19p684, 112p896, 232p1822, 232p1823, 661p1113, 661p1114, 842p2173

ZP(X(35),X(651)):
1, 37, 650, 2323, 9p1019, 11p2222

ZP(X(44),X(1)):
1, 100, 513, 100p537, 101p545, 109p528, 522p840, 527p919, 536p813, 665p1121, 739p812

ZP(X(55),X(190)):
6, 513, 518, 6p1027, 513p1381, 513p1382, 650p1381, 650p1382

ZP(X(57),X(294)):
1, 241, 651, 2254, 44p651, 88p2254, 514p1381, 514p1382, 518p1381, 518p1382, 527p840

ZP(X(100),X(657)):
7, 651, 883, 1462, 2p1381, 2p1382, 7p1381, 7p1382

ZP(X(101),X(522)):
1, 109, 1381, 1382, 104p999

ZP(X(105),X(241)):
1, 294, 650, 2p919, 9p1022, 9p1381, 9p1382, 105p1023, 528p2291, 885p1381, 885p1382

ZP(X(109),X(514)):
1, 101, 1381, 1382, 7p2283, 9p1381, 9p1382, 9p2195

ZP(X(109),X(655)):
101, 1381, 1382, 11p36

ZP(X(109),X(666)):
101, 1381, 1382, 11p1458

ZP(X(110),X(656)):
2, 112, 1113, 1114

ZP(X(112),X(656)):
4, 110, 1113, 1114, 1302p1725

ZP(X(112),X(661)):
2, 110, 1113, 1114, 2p1822, 2p1823, 3p293, 19p877

ZP(X(238),X(2)):
1, 6, 100, 649, 101p537, 106p899, 519p739

ZP(X(239),X(6)):
1, 2, 190, 513, 88p899, 100p537, 889p1960

ZP(X(240),X(63)):
1, 19, 162, 661, 30p111, 74p468, 110p1312, 110p1313, 112p542, 112p1312, 112p1313, 523p842

ZP(X(241),X(9)):
1, 57, 513, 651, 88p1155, 109p528, 514p840, 1121p1404

ZP(X(297),X(48)):
2, 4, 523, 648, 30p897, 162p542, 162p1312, 468p2349, 662p1312, 842p1577

ZP(X(350),X(42)):
2, 75, 514, 668, 88p536, 190p537, 889p1635

ZP(X(385),X(1)) [Brocard (first) cubic, K017] :
2, 6, 99, 512, 111p2234

ZP(X(401),X(19)):
2, 3, 520, 648, 852p2349

ZP(X(450),X(1)):
3, 4, 647, 648, 852p897

ZP(X(511),X(92)):
3, 6, 110, 647, 74p896, 110p2247, 163p1312, 163p1313, 656p842, 895p2173

ZP(X(512),X(31)):
2, 385, 538, 1916, 10p2106, 75p729, 274p2107, 297p1957 (no collinearities found)

ZP(X(512),X(75)):
6, 111, 187, 232, 248, 385, 2p1927, 6p1757, 6p1758, 6p1929, 13p2152, 14p2151, 19p450, 48p1942, 71p422, 74p2247, 82p2076, 421p1820, 425p1400, 543p923, 842p2173, 843p896, 2080p2186

ZP(X(513),X(1)) [ K137]:
1, 44, 88, 239, 241, 292, 294, 1931, 2p2054, 6p447, 106p545, 527p840, 528p2291, 537p739, 1280p1743

ZP(X(513),X(8)):
6, 57, 2291, 6p1323, 13p2307, 15p2306, 554p2152, 559p2154

ZP(X(514),X(31)):
2, 291, 350, 447, 519, 2p241, 2p294, 2p1932, 10p1929, 88p545, 145p1280, 528p1156

ZP(X(514),X(55)):
1, 7, 1156, 1323, 13p1082, 14p559, 15p1081, 16p554

ZP(X(514),X(81)):
2, 42, 55, 226, 519, 672, 10p105, 37p106

ZP(X(518),X(57)):
1, 9, 100, 650, 44p1156, 100p2246, 522p840, 527p2316

ZP(X(520),X(31)):
2, 401, 1972, 63p450, 92p852, 92p1942, 226p416, 325p1958

ZP(X(520),X(92)):
3, 6, 74, 3p2173

ZP(X(521),X(1)):
9, 57, 1944, 1945

ZP(X(521),X(4)):
1, 3, 2338, 63p1456

ZP(X(521),X(31)):
2, 448, 1944, 1952, 63p425, 92p416

ZP(X(521),X(81)):
9, 65, 2182, 2331, 10p102, 10p1433

ZP(X(521),X(92)):
3, 6, 221, 268, 2182, 3p102, 48p1325

ZP(X(522),X(31)):
2, 527, 673, 1121, 1948, 2p296, 2p518, 63p415, 88p528, 694p1281

ZP(X(522),X(55)):
2, 57, 527, 2p103, 2p1456, 7p1419, 7p2291

ZP(X(522),X(56)):
2, 9, 527, 8p2291, 283p1832, 283p1833, 1793p1832, 1793p1833

ZP(X(522),X(63)):
1, 19, 102, 208, 282, 4p2182, 6p1325

ZP(X(522),X(81)):
1, 19, 102, 208, 282, 4p2182, 6p1325

ZP(X(523),X(1)) [a Brocard cubic, K018]:
2, 6, 13, 14, 15, 16, 111, 368, 524, 530p2153, 531p2154

ZP(X(523),X(31)) [ K185]:
2, 287, 297, 524, 671, 694, 2p1757, 2p1758, 2p1929, 2p1966, 63p1942, 92p450, 94p1094, 94p1095, 226p425, 306p422, 542p2349, 543p897

ZP(X(523),X(63)):
4, 6, 74, 1990

ZP(X(523),X(91)):
371, 372, 47p94

ZP(X(523),X(92)):
3, 6, 50, 265

ZP(X(524),X(31)):
2, 99, 523, 162p542, 543p662, 843p1577

ZP(X(525),X(19)):
2, 3, 30, 3p2349

ZP(X(525),X(31)):
2, 30, 98, 325, 1494, 3p1956, 72p447, 92p401, 226p448, 441p2184, 542p897, 1297p1895

ZP(X(525),X(48)):
2, 4, 30, 4p2349

ZP(X(525),X(63)):
2, 25, 30, 1073, 1297, 4p204, 4p2159, 4p2312

ZP(X(527),X(31)):
2, 522, 664, 44p666, 88p918, 100p528, 693p840

ZP(X(528),X(31)):
2, 666, 918, 7p1023, 8p1022, 100p527, 513p1121

ZP(X(536),X(31)):
2, 513, 668, 88p812, 100p537, 335p1023

ZP(X(537),X(31)):
2, 812, 1022, 2p660, 44p668, 100p536, 693p739

ZP(X(542),X(92)):
3, 6, 879, 110p1755

ZP(X(647),X(75)):
6, 74, 511, 1495, 1976, 4p1955, 48p1987, 111p2247, 204p1297, 228p447, 441p2155, 448p1400, 765p866, 842p896

ZP(X(647),X(91)):
371, 372, 511, 24p293

ZP(X(649),X(1)):
1, 238, 291, 899, 2107, 2p739, 2p2106, 3p422, 105p1983, 106p537, 1463p2053

ZP(X(649),X(58)):
1, 10, 726, 899, 2p192, 10p727, 37p2162, 321p739

ZP(X(649),X(75)):
6, 106, 238, 902, 1326, 1458, 1911, 2054, 2195, 31p447, 840p1155, 2246p2291

ZP(X(650),X(1)) [Pelletier strophoic, K040]:
1, 105, 243, 296, 518, 1155, 1156, 3p415, 80p202, 80p203, 88p2246, 519p840, 1281p1967

ZP(X(650),X(7)):
1, 55, 1155, 9p2291, 13p1250, 15p1251, 1833p2193

ZP(X(650),X(8)):
1, 56, 103, 1155, 1456, 56p1156, 57p1419

ZP(X(652),X(1)):
1, 1936, 1937, 3p425, 4p416, 6p448

ZP(X(652),X(75)):
55, 56, 1936, 6p1945

ZP(X(656),X(1)):
1, 1910, 1959, 2173, 2349, 3p1987, 4p401, 64p441, 65p448, 71p447, 111p542, 449p2213, 524p842, 866p1016, 1249p1297

ZP(X(659),X(1)):
1, 2, 6, 88p899, 519p739, 730p743, 731p742

ZP(X(661),X(1)):
1, 240, 293, 896, 897, 1757, 1758, 1929, 1967, 3p1942, 4p450, 13p16, 14p15, 30p842, 65p425, 68p421, 72p422, 74p542, 83p2076, 99p804, 111p543, 262p2080, 524p843, 1687p2010, 1688p2009

ZP(X(661),X(75)):
1, 31, 896, 923, 2151, 2152, 2153, 2154

ZP(X(663),X(75)):
6, 672, 1055, 1438, 1949, 2202, 2291, 44p840, 48p415, 103p1419, 106p2246, 202p2161, 203p2161

ZP(X(665),X(75)):
6, 55, 56, 840, 1083, 6p2246, 44p2291, 88p1055, 761p2239

ZP(X(667),X(86)):
6, 37, 192, 1575, 6p899, 10p739, 37p727, 42p2162

ZP(X(669),X(75)):
6, 694, 729, 1691, 6p2234, 42p2106, 81p2107, 232p1957

ZP(X(669),X(82)):
6, 141, 698, 6p2234, 38p699, 75p194, 729p1930

ZP(X(672),X(85)):
6, 55, 101, 663, 44p2291, 101p2246, 650, 840, 1055p1320

ZP(X(798),X(1)):
1, 1580, 1581, 2234, 2p729, 37p2106, 86p2107, 240p1957   (no collinear triples)

ZP(X(812),X(31)):
1, 2, 75, 537, 88p536, 889p1969

ZP(X(822),X(1)):
1, 1955, 1956, 3p450, 4p852, 4p1942, 65p416, 511p1975   (no collinear triples)

ZP(X(894),X(100)):
2, 42, 239, 649, 2p875, 81p514

ZP(X(894),X(101)):
1, 10, 239, 514, 876, 1019, 514p1381, 514p1382, 522p1381, 522p1382

ZP(X(896),X(1)):
1, 661, 662, 110p543, 112p542, 523p843, 525p842, 538p805, 729p804, 1022p1757, 1023p1929

ZP(X(902),X(75)):
6, 101, 649, 59p1643, 101p537, 545p692, 650p840, 659p739, 665p1156, 813p899, 919p1155

ZP(X(918),X(31)):
2, 7, 8, 528, 44p1121, 75p840, 75p1083, 88p527

ZP(X(918),X(57)):
1, 2, 9, 55, 57, 200, 528, 9p840, 149p1110

ZP(X(928),X(92)):
3, 6, 2066, 2067, 9p2067, 57p2066

ZP(X(1001),X(100)):
1, 6, 513, 514, 518, 1027

ZP(X(1055),X(75)):
6, 109, 663, 44p919, 88p665, 101p2246, 513p840

ZP(X(1146),X(59)):
513, 522, 676, 9p1638, 11p677, 513p1156, 514p1419

ZP(X(1155),X(1)):
1, 650, 651, 88p2254, 100p2246, 105p1023, 514p840

ZP(X(1577),X(31)):
1, 75, 897, 2p13, 2p14, 2p15, 2p16, 2p524, 13p530, 14p531

ZP(X(1580),X(75)):
1, 31, 662, 798, 524p729, 691p888

ZP(X(1757),X(81)):
1, 37, 100, 661, 44p897, 690p901

ZP(X(1797),X(44)):
2, 1113, 1114

ZP(X(1914),X(76)):
6, 31, 101, 667, 44p739, 537p692

ZP(X(1931),X(37)):
1, 81, 513, 662, 88p896, 691p900

ZP(X(1959),X(19)):
1, 63, 656, 662, 30p895, 74p524, 110p542, 110p1312, 110p1313, 525p842

ZP(X(1963),X(100)):
81, 661, 1931, 1962, 514p1171, 514p2054

ZP(X(1966),X(31)):
1, 75, 799, 6p523, 111p538, 351p886

ZP(X(2106),X(10)):
6, 81, 99, 667, 739p2234

ZP(X(2173),X(1)):
1, 162, 656, 110p542, 523p842, 691p868, 866p898, 867p901, 1304p1651

ZP(X(2234),X(1)):
1, 798, 799, 111p804, 524p805

ZP(X(2243),X(1)):
1, 1491, 1492, 716p795, 717p794

ZP(X(2254),X(1)):
1, 9, 57, 2246, 2p840, 2p1083, 44p1156, 88, 1155, 742p761, 743p760

ZP(X(2254),X(85)):
1, 6, 41, 55, 56, 220, 2246, 55p840, 654p1308

ZP(X(2284),X(109)):
11, 100, 1001, 522p1002, 522p1381, 522p1382, 644p2350, 1111p1621


H(U,P): Hirst Cubics

   [(rv2w - qw2u)y - (qw2v - rv2u)z]x2
+ [(pw2u - ru2v)z - (ru2w - pw2v)x]y2
      + [(qu2v - pv2w)x - (pv2u - qu2w )y]z2 = 0

H(X(2),X(1)) ( = Z(X(239),X(6))):
1, 2, 6, 75, 239, 291, 366, 518, 673, 1575, 2319, 2p1423, 2p1932, 2p2054, 2p2106, 2p2107, 2p2108, 2p2109, 2p2110, 2p2111, 2p2112, 2p2114, 2p2115, 2p2116, 2p2117, 2p1118, 2p1119, 2p2144, 2p2145, 2p2146, 2p2147, 75p727, 694p1281, 1655p2248

H(X(2),X(10)):
1, 2, 7, 37, 291, 335, 350, 518, 694, 1909, 2p1757, 8p292, 10p2248, 28p337, 87p1575, 105p335, 239p2113, 291p292, 291p1929, 292p1281, 726p2109

H(X(2),X(63)):
2, 3, 57, 291, 447, 517, 1944

H(X(2),X(76)):
2, 8, 75, 239, 256, 274, 291, 350, 740, 1281, 2p673, 2p1447, 2p1929, 2p1966, 86p1654, 238p1921, 239p518, 334p2112, 350p1757

H(X(2),X(85)):
2, 7, 8, 279, 291, 508, 516, 673, 2p241, 2p1279, 2p1447, 2p2114, 7p1280, 85p103, 85p2115, 330p1742

H(X(2),X(92)):
2, 4, 278, 291, 447, 515, 1948

H(X(3),X(1)):
1, 3, 4, 255, 296, 416, 1936, 3p415, 90p1745, 1046p1248

H(X(3),X(101)):
3, 109, 296, 651, 1783, 2196, 2338, 3p1020

H(X(4),X(1)):
1, 3, 4, 158, 243, 415, 1937, 4p416, 90p1148, 1047p1247

H(X(6),X(1)) ( = Z(X(238),X(2))):
1, 2, 6, 31, 105, 238, 292, 365, 672, 1423, 1931, 2053, 2054, 2106, 2107, 2108, 2109, 2110, 2111, 2112, 2113, 2114, 2115, 2116, 2117, 2118, 2119, 2144, 2145, 2146, 2147, 2p727, 6p1575, 1045p2248, 1281p1967

H(X(6),X(3)):
6, 55, 58, 63, 103, 292, 511, 672, 1423, 3p862, 8p904

H(X(6),X(32)):
6, 31, 58, 238, 292, 727, 893, 1691, 1914, 2176, 2195, 3p862, 6p2068, 6p2069, 58p1045, 81p2107, 87p1914, 105p2110, 238p1458, 238p1914, 726p2210

H(X(6),X(36)):
6, 292, 840, 902, 1423, 2163, 2p36

H(X(6),X(40)):
6, 292, 672, 937, 972, 1423, 2p40, 2p1911, 3p55

H(X(6),X(41)):
6, 55, 56, 105, 292, 1914, 2110, 2223, 2p1911, 6p2111

H(X(6),X(48)):
3, 6, 56, 104, 292, 1951, 2223, 2p1911, 48p422, 956p2279

H(X(6),X(56)):
6, 56, 57, 292, 672, 1423, 1458, 1477, 2195, 2223, 2p1911, 6p1743, 57p1362, 87p2223, 103p1419, 103p2114, 238p1458, 672p1279

H(X(6),X(58)):
6, 58, 81, 292, 741, 1326, 1911, 2106, 2p1911, 3p862, 292p1929, 741p2107

H(X(7),X(1)):
7, 55, 174, 241, 673, 1088, 2p1742, 503p1488

H(X(7),X(85)):
7, 8, 279, 291, 508, 516, 673, 2p241, 2p1279, 2p1447, 7p1280, 85p103, 85p2115, 330p1742

H(X(9),X(1)) ( = Z(X(518),X(57)) ):
1, 9, 57, 200, 239, 294, 518, 1280, 1282, 2348, 2p103, 2p2115, 8p1911, 9p509, 8p910, 1742p2319

H(X(19),X(1)):
1, 19, 63, 240, 1096, 1910, 1967, 2312, 2p419, 2p1692, 4p401, 4p1297, 25p147, 64p193, 297p2065

H(X(31),X(1)):
1, 6, 31, 75, 560, 1403, 1580, 1755, 1910, 1967, 2053, 2p699, 4p1613, 25p147, 31p2227, 83p2076, 1281p1911

H(X(31),X(32)):
6, 31, 213, 1911, 1922, 1967, 2210, 6p172, 6p741, 6p1458, 6p2162, 31p1575, 43p1911, 213p2106, 291p1911, 292p727, 292p2195, 741p2107, 1911p2068, 1911p2069, 2111p2223

H(X(37),X(1)):
1, 37, 81, 291, 756, 1654, 1757, 2238, 2p2054, 2p2108, 37p2109, 37p2248

H(X(37),X(10)):
2, 10, 37, 210, 740, 1654, 2238, 2p1284, 2p2054, 10p105, 10p385, 10p904, 10p1911, 37p2238, 42p1281, 239p740, 518p2238, 740p1757, 1655p2107

H(X(42),X(1)):
1, 42, 86, 292, 872, 2107, 2110, 2238, 6p1045, 37p2106, 37p2111

H(X(42),X(9)):
42, 333, 756, 2107, 2161, 2238, 2258, 6p1045

H(X(55),X(1)):
1, 7, 55, 259, 294, 672, 1253, 9p1742

H(X(57),X(1)):
1, 9, 57, 105, 241, 269, 292, 509, 910, 1279, 1447, 2114, 2p1477, 7p103, 7p2115, 87p,1742, 355p1355

H(X(57),X(56)):
1,6, 57, 105, 1279, 1429, 1462, 2162, 2p1462, 7p1458, 105p291, 105p294, 105p1743, 192p1462, 269p1376, 673p1477

H(X(63),X(1)):
1, 19, 63, 293, 326, 1959, 2p401, 2p1297, 3p230, 3p694, 3p1503, 6p147, 69p419, 193p1073, 194p1988, 325p2065

H(X(65),X(1)):
1, 21, 65, 851, 1254, 1758, 1937, 4p1046, 73p1247

H(X(75),X(1)):
1, 2, 31, 75, 561, 1581, 1821, 1959, 1966, 2227, 2p1423, 2p2319, 4p147, 4p194, 76p699, 291p1281, 308p2076

H(X(75),X(76)):
2, 10, 75, 85, 334, 335, 1581, 1920, 1921, 2p518, 8p291, 27p337, 75p1757, 87p726, 105p334, 291p291, 291p1281, 321p2248, 335p1929, 350p2113

H(X(81),X(1)):
1, 37, 81, 238, 757, 1929, 1931, 2109, 2248, 2p741, 81p1654, 86p2108

H(X(105),X(1)):
1, 6, 57, 105, 294, 518, 673, 910, 1376, 87p238, 103p673, 105p105, 105p165, 673p1742, 1447p2115

H(X(240),X(1)):
1, 19, 92, 240, 293, 1581, 1707, 1755, 1959, 4p194, 6p114, 132p1073, 232p385, 232p297, 282p385, 240p1957, 262p1351, 297p2065, 1249p1297

H(X(241),X(1)):
1, 7, 57, 241, 291, 294, 518, 672, 1743, 2p1423, 2p1477, 7p1362, 87p672, 238p241, 241p2348

H(X(243),X(1)):
1, 4, 29, 46, 243, 296, 851, 1936, 4p450, 29p1046, 90p243, 243p243, 243p1758, 851p1247, 1936p1942

H(X(293),X(1)):
1, 48, 63, 240, 293, 1580, 1821, 1910, 1957, 2p2065, 3p230, 3p230, 64p441, 98p194, 193p248, 248p1916, 401p1988

H(X(294),X(1)):
1, 9, 55, 105, 238, 241, 294, 673, 2053, 2348, 43p673, 57p1376, 105p1280, 145p2195, 291p294, 294p294, 514p1293, 516,2115

H(X(296),X(1)):
1, 3, 73, 90, 243, 296, 1758, 1937, 1940, 2p2249, 3p1942, 46p296, 73p1247, 296p292

H(X(518),X(1)):
1, 2, 9, 105, 165, 241, 518, 672, 2p103, 2p1742, 8p1362, 43p291, 59p1566, 291p1282, 518p1376, 1280p1743

H(X(672),X(1)):
1, 6, 55, 241, 292, 518, 672, 673, 55p1362, 238p518, 291p2110

H(X(673),X(1)):
1, 2, 7, 105, 239, 294, 672, 673, 105p291, 239p2111, 673p673


HP(U,P): H-Plus Cubics

   [(rv2w + qw2u)y - (qw2v + rv2u)z]x2
+ [(pw2u + ru2v)z - (ru2w + pw2v)x]y2
      + [(qu2v + pv2w)x - (pv2u + qu2w )y]z2 = 0

HP(X(1),X(2)) ( = Z(X(86),X(42)) ):
1, 2, 7, 21, 29, 77, 81, 86, 2p1433, 4p1817, 20p84, 253p2360, 1034p1394

HP(X(1),X(20)):
1, 8, 20, 21, 29, 78, 280, 1043, 3p1034, 4p1819, 29p1490, 64p1043, 271p1712,

HP(X(1),X(40)) ( = Z(X(8),X(56)) ):
1, 8, 40, 175, 176, 188, 280, 483, 2p2066, 8p2067, 8p2362, 9p557, 92p2066, 164p188, 188p505

HP(X(1),X(57)) ( = HP(X(1),X(40)) ):
1, 2, 7, 57, 145, 174, 1488, 2089, 145p2137

HP(X(1),X(63)) ( = Z(X(75),X(31)) ):
1, 2, 7, 8, 63, 75, 92, 280, 347, 1895, 2p1073, 189p1490, 223p1034, 253p1498, 1032p1249

HP(X(2),X(1)) ( = Z(X(894),X(6)) ):
6, 7, 9, 37, 75, 86, 87, 192, 256, 366, 894, 1045, 1654, 2p2248, 1575p1929

HP(X(2),X(2)) ( = Z(X(2),X(58)) ):
1, 2, 9, 10, 37, 226, 281, 1214, 2p2331, 10p1433, 20p1903, 40p2184, 1490p2184

HP(X(3),X(1)):
4, 21, 73, 90, 255, 1046, 1248, 1745, 1935, 3p46, 3p1047, 3p1247, 1936p1942

HP(X(3),X(3)):
1, 3, 73, 1745, 3p73

HP(X(4),X(1)):
3, 29, 46, 65, 158, 1047, 1148, 1247, 1940, 4p90, 4p1046, 4p1248, 243p1942

HP(X(4),X(4)):
1, 4, 46, 65, 225, 2362, 10p2362, 46p254, 90p225, 225p1806, 485p2362

HP(X(5),X(5)):
1, 5, 5p35, 5p65, 5p73, 5p2307, 319p2181, 484p1263, 559p1953, 655p2081

HP(X(6),X(1)) ( = Z(X(171),X(2)) ):
2, 31, 42, 43, 55, 57, 81, 171, 365, 846, 893, 2162, 2248, 6p1045, 1282p2111

HP(X(6),X(6)):
1, 6, 42, 43, 213, 42p2162

HP(X(7),X(7)):
1, 7, 57, 142, 354, 2p1418, 7p2191, 142p218

HP(X(8),X(1)):
40, 56, 188, 280, 341, 979, 1050, 1222, 2p2347, 8p978

HP(X(8),X(8)):
1, 8, 40, 2p2347, 40p2123, 312p2347

HP(X(9),X(1)):
2, 43, 55, 57, 165, 200, 1376, 2319, 9p509, 9p1742, 9p1743, 103p239, 514p1293

HP(X(9),X(9)):
1, 9, 55, 165, 220, 2066, 9p365, 9p2067, 55p1489, 165p2125, 200p2362, 281p2066

HP(X(10),X(10)):
1, 10, 191, 2292, 10p2067, 10p2292, 12p1806, 191p2127, 502p2292

HP(X(13),X(13)):
1, 13, 3p1832, 10p2306, 13p202, 45p1987, 196p249, 967p1972, 1081p1956, 1807p1833, 1956p1987

HP(X(14),X(14)):
1, 14, 3p1833, 14p203, 37p554, 1807p1832

HP(X(19),X(1)):
31, 63, 92, 204, 1096, 1707, 1957, 1957, 2184, 4p1613, 4p1988, 230p1987, 419p1297, 694p1503

HP(X(19),X(19)):
1, 19, 31, 1707, 1973, 6p371, 6p372, 6p2362, 19p2066, 25p584, 25p486, 33p2067, 34p2066, 1707p2129

HP(X(20),X(20)):
1, 1394, 4p1394, 10p1394, 20p73, 20p207, 20p221, 20p1042, 1042p1097

HP(X(21),X(21)):
1, 3, 21, 283p407, 407p1098

HP(X(24),X(24)):
1, 24, 24p65, 24p73, 24p1062, 24p1479

HP(X(25),X(25)):
1, 25, 1402, 1716, 4p1402, 6p2082, 19p2082, 42p614, 1851p1918

HP(X(27),X(27)):
1, 27, 57, 58, 278, 579, 1474, 1838, 2260, 2p942, 21p2260, 27p2260, 272p1841, 284p1838, 580p942

HP(X(28),X(28)):
1, 28, 34, 56, 1104, 1724, 21p1104, 21p1842, 25p272, 28p1104, 404p1842

HP(X(30),X(30)):
1, 30, 30p36, 30p65, 30p73, 30p1464, 30p1870, 758p1354

HP(X(31),X(1)):
6, 19, 48, 75, 82, 560, 1582, 1740, 1964, 6p695, 32p1031

HP(X(31),X(31)):
1, 31, 1740, 1923, 1964

HP(X(33),X(33)):
1, 33, 1721, 55p1836

HP(X(34),X(34)):
1, 34, 1722, 56p1837, 1398p1837

HP(X(37),X(37)):
1, 37, 846, 1962, 37p1251, 37p1962, 554p1334, 559p1962, 846p2135, 1082p1962

HP(X(40),X(40)):
1, 40, 221, 40p221, 40p266, 40p2067, 40p2362, 175p221, 176p221, 196p2066, 198p557, 198p558, 223p2066

HP(X(55),X(55)):
1, 55, 1742, 2293, 41p1212

HP(X(56),X(1)):
8, 84, 221, 266, 978, 1106, 1201, 1476, 56p979, 56p1050

HP(X(56),X(56)):
1, 56, 978, 1201, 31p1122

HP(X(56),X(57)):
2, 28, 57, 603, 978, 1201, 1407

HP(X(57),X(1)):
6, 7, 9, 87, 269, 509, 1419, 1423, 1742, 1743, 57p1376, 103p1447, 291p910

HP(X(57),X(57)):
1, 6, 56, 57, 266, 289, 1743, 6p2089, 1743p2137

HP(X(63),X(1)):
19, 48, 75, 326, 610, 1740, 1958, 2p1073, 2p1988, 3p193, 385p1297, 441p694

HP(X(63),X(63)):
1, 3, 48, 63, 219, 222, 255, 268, 610, 3p223, 3p1073, 154p1032, 271p1035, 1073p1498

HP(X(65),X(65)):
1, 65, 1046, 3p407, 73p407

HP(X(69),X(69)):
1, 69, 72, 306, 1439, 1763, 2p1473, 7p1040, 8p1040, 10p1473, 20p1439, 307p1040, 1763p2139

HP(X(75),X(1)):
2, 31, 38, 63, 92, 561, 1965, 2p83, 2p194, 2p695, 6p1031

HP(X(75),X(75)):
1, 38, 63, 75, 1930, 2p427, 22p427, 66p69, 66p1370, 141p1342, 141p1343

HP(X(81),X(1)):
6, 37, 86, 757, 1100, 1963, 2p1171, 2p2248, 58p1654, 81p1051

HP(X(81),X(2)):
1, 10, 58, 1029, 2p2363, 593p596, 1269p2220

HP(X(81),X(81)):
1, 6, 81, 1100, 21p553, 58p1125, 596p1333, 1269p2220

HP(X(91),X(91)):
1, 91, 2p216, 3p486, 4p486, 4p637, 4p638, 5p68, 5p485, 5p486, 68p372

HP(X(100),X(100)):
1, 100, 513, 1381, 1382, 522p1381

HP(X(101),X(101)):
1, 41, 101, 663, 41p508, 513p1621

HP(X(105),X(105)):
1, 105, 238, 1279, 105p1279

HP(X(109),X(109)):
1, 109, 603, 1459, 3p1381, 3p1382, 65p1822, 65p1823, 513p1381, 513p1382, 513p1822, 513p1823, 514p572

HP(X(110),X(110)):
1, 110, 9p1019, 21p1399, 35p109, 35p513, 655p2290

HP(X(162),X(162)):
1, 162, 656, 1822, 1823, 110p1312, 110p1313, 523p1113, 523p1114

HP(X(163),X(163)):
1, 163, 810, 3p32, 3p1379, 3p1380, 512p1078, 512p1379, 512p1380

HP(X(171),X(171)):
1, 171, 894, 3p444, 43p894, 58p894, 63p444, 72p444

HP(X(174),X(174)):
1, 173, 174, 177, 236, 3p2091, 6p178, 177p258

HP(X(189),X(189)):
1, 4, 57, 1422, 2262, 2270, 4p282, 6p309, 63p1856, 77p2262, 84p946, 280p2262

HP(X(220),X(9)):
7, 9, 480, 9p1200, 218p220

HP(X(226),X(226)):
1, 37, 65, 226, 442, 1781, 2294, 7p2294, 10p2160, 12p942, 73p445, 500p502

HP(X(271),X(271)):
1, 3, 271, 1433, 3p1854, 9p1073, 78p1854, 271p1854

HP(X(326),X(326)):
1, 326, 2p1498, 3p1899, 69p426, 426p1032

HP(X(329),X(329)):
1, 196, 329, 2324, 40p1108, 196p1490, 223p1210, 1103p1210

HP(X(333),X(333)):
1, 8, 9, 283, 284, 333, 573, 2269, 2p960, 4p960, 21p960, 21p1193, 60p1211, 386p2339, 572p960

HP(X(365),X(365)):
1, 365, 3p367, 365p367

HP(X(366),X(366)):
1, 364, 366, 367, 366p367

HP(X(385),X(385)):
1, 385, 10p1580, 10p1691, 238p1580, 239p1966, 385p1284, 1281p1691

HP(X(394),X(394)):
1, 394, 836, 3p71, 3p72, 81p836, 86p836, 394p836

HP(X(484),X(484)):
1, 15p484, 16p484, 36p484, 58p484, 106p484, 203p484, 214p484, 484p501, 484p758, 484p1130

HP(X(513),X(513)):
1, 244, 513, 764, 1054

HP(X(515),X(515)):
1, 515, 1455, 40p1455, 80p1455, 515p517, 515p1457, 517p1359

HP(X(651),X(651)):
1, 650, 651, 9p1381, 9p1382, 514p1381, 514p1382

HP(X(662),X(662)):
1, 662, 2p1379, 2p1380, 6p1113, 6p1114, 110p1312, 110p1313, 313p1919, 523p1380, 525p1113, 525p1114

HP(X(664),X(664)):
1, 514, 664, 7p1376, 513p1376, 651p1376, 693p1037, 1376p1633

HP(X(666),X(666)):
1, 239, 294, 644, 666, 885, 9p659, 31p874, 105p812, 190p2348, 239p294, 740p919

HP(X(765),X(765)):
1, 100, 765, 3p1862, 1331p1862

HP(X(775),X(775)):
1, 255, 775, 3p1885, 1105p1885

HP(X(811),X(811)):
1, 811, 1577, 4p1975, 99p1968, 512p1975

HP(X(813),X(813)):
1, 811, 1577, 4p1975, 99p1968, 512p1975

HP(X(894),X(894)):
1, 171, 894, 2329, 58p1920, 171p1107, 894p1107, 1197p1215

HP(X(901),X(901)):
1, 36, 106, 109, 901, 2p1983, 6p1019, 6p1022, 36p106, 36p513, 59p1769, 88p654

HP(X(908),X(908)):
1, 119, 517, 908, 6p119, 6p153, 8p2183, 57p119, 80p1465, 119p517, 119p2323

HP(X(920),X(920)):
1, 155, 920, 3p155, 3p454, 46p155, 90p155, 155p371, 155p372, 155p485, 155p487, 155p488, 493p1609, 494p1609, 920p1124, 920p1335

HP(X(1010),X(1010)):
1, 388, 1010, 1038, 388p958, 388p960, 940p2303, 1010p1193

HP(X(1025),X(1025)):
1, 1025, 2283, 2284, 103p241, 241p926, 241p2254, 518p1362, 518p2254, 672p1280, 918p1381, 918p1382, 1381p2254, 1382p2254

HP(X(1150),X(1150)):
1, 1150, 10p993, 10p2278, 993p995, 995p1150

HP(X(1171),X(1171)):
1, 6, 58, 1171, 37p1126, 37p1203, 81p1203, 1126p1203, 1203p1255

HP(X(1309),X(1309)):
1, 104, 108, 1309, 104p522, 108p515

HP(X(1381),X(1381)):
1, 56, 266, 1381, 513p1382

HP(X(1400),X(1400)):
1, 213, 1400, 1402, 2092, 6p2092, 37p904, 56p2292, 73p444, 181p2300

HP(X(1423),X(1423)):
1, 1403, 1423, 2176, 43p982, 43p2275, 982p1423

HP(X(1445),X(1445)):
1, 218, 1445, 1617, 9p218, 55p218, 218p218

HP(X(1708),X(1708)):
1, 1708, 3p1708, 6p1708, 35p1780, 37p1780, 71p1780, 72p1780

HP(X(1737),X(1737)):
1, 119, 912, 1737, 3p119, 36p119, 46p912, 80p912, 90p119, 119p912

HP(X(1740),X(1740)):
1, 194, 1740, 2p194, 43p194, 87p194, 194p194

HP(X(1748),X(1748)):
1, 563, 1748, 2p571, 2p1147, 4p571, 24p1147, 155p1993, 254p571

HP(X(1749),X(1749)):
1, 1749, 3p1157, 35p1749, 36p1749, 195p1157, 1094p1749, 1095p1749, 1154p1157

HP(X(1760),X(1760)):
1, 3p22, 4p206, 6p206, 22p206, 22p1677, 206p1670, 206p1671

HP(X(1761),X(1761)):
1, 1761, 3p199, 27p199, 58p199, 58p1330, 199p2248

HP(X(1762),X(1762)):
1, 1762, 21p1762, 31p1762, 48p1762, 1172p1762, 1762p2194

HP(X(1953),X(1953)):
1, 1953, 6p233, 17p51, 18p51, 51p233, 62p233

HP(X(1958),X(1958)):
1, 1957, 1958, 2p1975, 20p1968, 194p1975, 1196p1975

HP(X(2155),X(2155)):
1, 1973, 2155, 6p800, 19p2155, 64p185

HP(X(2160),X(2160)):
1, 2160, 2308, 6p1251, 41p554, 554p2308, 1081p2308, 2160p2308

HP(X(2166),X(2166)):
1, 1725, 1749, 2166, 265p403

HP(X(2222),X(2222)):
1, 513, 859, 1319, 1769, 2222, 10p1411, 11p2222, 59p1769, 80p1457, 517p1168, 517p2222

HP(X(2285),X(2285)):
1, 1460, 2285, 6p612, 171p1010, 388p1468, 388p2268, 612p1468, 1999p2303

HP(X(2287),X(2287)):
1, 200, 220, 2287, 2p2332, 9p2264, 20p2332, 21p950, 21p2264, 78p2264

HP(X(2311),X(2311)):
1, 41, 2311, 8p237, 9p1967, 21p2223, 240p1808

HP(X(2316),X(2316)):
1, 2316, 9p2183, 15p1251, 1833p2193

HP(X(2319),X(2319)):
1, 8, 2319, 2p2319, 9p2275, 41p982, 2053p2275


C(U,L): Cross Conjugate Collinearity Cubics

L(wy + vz)x2 + M(uz + wx)y2 + N(vx + uy)z2 - (Lu + Mv + Nw)xyz = 0

C(X(25),L(1,2)):
4, 101, 1113, 1114, 37p1113, 37p1114

C(X(56),L(1,2)):
57, 100, 1381, 1382, 2p1381, 2p1382, 1280p1617

C(X(764),L(1,2)):
513, 514, 900, 1022

C(X(1470),L(1,2)):
100, 104, 109, 2p997, 2p1381, 2p1382, 2p1470, 997p1381, 997p1382

C(X(255),L(1,3)):
63, 1822, 1823, 3p109, 1214p1822, 1214p1823

C(X(3),L(1,4)):
2, 109, 1113, 1114, 226p1822, 226p1823

C(X(56),L(1,4)):
57, 108, 1381, 1382, 19p2338, 278p1381, 278p1382, 658p1456

C(X(255),L(1,4)):
57, 108, 1381, 1382, 19p2338, 278p1381, 278p1382, 658p1456

C(X(56),L(1,5)):
57, 1381, 1382, 2222, 1381p2006, 1382p2006

C(X(255),L(1,5)):
63, 1822, 1823, 3p2222

C(X(41),L(1,6)):
55, 101, 1381, 1382, 220p1381, 220p1382

C(X(48),L(1,6)):
3, 101, 1381, 1382, 55p2338, 219p1381, 219p1382

C(X(56),L(1,6)):
1, 57, 1381, 1382

C(X(73),L(1,6)):
101, 1214, 1381, 1382, 72p1381, 72p1382

C(X(172),L(1,6)):
101, 171, 1381, 1382, 1381p2329, 1382p2329

C(X(198),L(1,6)):
40, 101, 1381, 1382, 1381p2324, 1382p2324

C(X(255),L(1,6)):
63, 906, 1822, 1823, 72p1822, 72p1823

C(X(604),L(1,6)):
56, 101, 1381, 1382, 6p1381, 6p1382, 218p1477, 1279p1292

C(X(56),L(1,7)):
6, 651, 1020, 1400, 2p1381, 2p1382, 6p2283, 10p1462, 1381p1400, 1382p1400

C(X(213),L(1,7)):
6, 651, 1020, 1400, 2p1381, 2p1382, 6p2283, 10p1462, 1381p1400, 1382p1400

C(X(220),L(1,7)):
9, 651, 1815, 2p1381, 2p1382, 9p1381, 9p1382, 100p1886

C(X(255),L(1,7)):
63, 1822, 1823, 3p934

C(X(603),L(2,3)):
58, 162, 222, 651, 2p104, 3p1381, 3p1382, 27p1381, 27p1382, 109p859

C(X(1464),L(2,3)):
1, 81, 278, 2p1983, 36p653, 100p1835

C(X(25),L(2,6)):
4, 110, 1113, 1114

C(X(51),L(2,6)):
5, 110, 1113, 1114, 5p1822, 5p1823

C(X(154),L(2,6)):
20, 110, 1113, 1114, 20p1822, 20p1823

C(X(159),L(2,6)):
110, 1113, 1114, 1370, 1370p1822, 1370p1823

C(X(161),L(2,6)):
110, 1113, 1114, 75p161

C(X(184),L(2,6)):
3, 110, 1113, 1114, 1370, 3p1822, 3p1823

C(X(206),L(2,6)):
22, 110, 1113, 1114, 1370, 22p1822, 22p1823, 255p1297

C(X(232),L(2,6)):
22, 110, 1113, 1114, 1370, 22p1822, 22p1823, 255p1297

C(X(311),L(2,6)):
76, 300, 301, 662

C(X(25),L(2,7)):
4, 109, 1113, 1114, 65p1113, 65p1114

C(X(31),L(2,7)):
1, 109, 1822, 1823, 65p1113, 65p1114, 104p1470

C(X(55),L(2,7)):
1, 100, 1381, 1382, 8p1381, 8p1382, 999p1320

C(X(222),L(2,7)):
77, 651, 2338, 7p1381, 7p1382, 63p1381, 63p1382

C(X(5),L(3,6)):
2, 13, 14, 1625

C(X(71),L(3,6)):
1, 906, 1822, 1823, 37p1822, 37p1823

C(X(2140),L(3,6)):
7, 86, 673, 692p2140

C(X(3),L(4,6)):
2, 112, 1113, 1114

C(X(15),L(4,6)):
112, 470, 1113, 1114

C(X(16),L(4,6)):
112, 471, 1113, 1114

C(X(32),L(4,6)):
25, 112, 1113, 1114, 923p1995, 1113p1973, 1114p1973

C(X(39),L(4,6)):
112, 427, 1113, 1114

C(X(50),L(4,6)):
112, 186, 1113, 1114

C(X(52),L(4,6)):
112, 467, 1113, 1114

C(X(58),L(4,6)):
27, 112, 1113, 1114, 28p1113, 28p1114

C(X(61),L(4,6)):
112, 473, 1113, 1114

C(X(62),L(4,6)):
112, 472, 1113, 1114

C(X(182),L(4,6)):
112, 458, 1113, 1114

C(X(187),L(4,6)):
112, 468, 1113, 1114

C(X(216),L(4,6)):
5, 112, 1113, 1114, 53p1822, 53p1823

C(X(284),L(4,6)):
29, 112, 1113, 1114, 1113p1172, 1114p1172

C(X(2193),L(4,6)):
21, 112, 1113, 1114, 284p1113, 284p1114


ZC(U,L): ZC-Cubics

L(wy - vz)x2 + M(uz - wx)y2 + N(vx - uy)z2 = 0

ZC(X(1),L(1,2)):
1, 190, 649, 2p1016

ZC(X(2),L(1,2)):
2, 190, 514, 1016, 1016p1054

ZC(X(1),L(1,3)):
1, 650, 651, 2p1262

ZC(X(1),L(1,4)):
1, 652, 653, 393p1275

ZC(X(1),L(1,5)):
1, 654, 655, 655p655

ZC(X(1),L(1,6)):
1, 100, 513, 765, 765p1054

ZC(X(6),L(1,6)):
1, 100, 667, 1016

ZC(X(279),L(1,7)):
279, 658, 1275, 244p658, 1054p1275, 1987p1987

ZC(X(2),L(2,3)):
2, 525, 648, 92p250

ZC(X(524),L(2,6)):
99, 524, 1649, 662p892, 1379p1577, 1380p1577

ZC(X(100),L(2,11)):
100, 190, 664, 666, 2284, 2p919, 6p874, 8p919, 105p660, 666p673

ZC(X(110),L(2,11)):
99, 110, 648, 666, 919m 48p666

ZC(X(658),L(2,11)):
651, 658, 664, 666, 883, 927, 2p927, 105p927, 165p927, 190p1456, 664p1376, 932p1447

ZC(X(665),L(2,11)):
1, 101, 514, 665, 666, 1026, 1027, 2p1279, 6p1280, 10p1438, 21p241

ZC(X(1638),L(2,11)):
2, 514, 527, 651, 666, 673, 918, 1638, 2p1027, 2p1279, 2p1308, 100p527, 105p527, 190p1456, 513p1121, 527p885, 666p1155

ZC(X(1639),L(2,11)):
2, 519, 522, 644, 666, 918, 1639, 2p294, 2p2342, 7p1023, 8p910, 8p1022, 8p1024, 8p2222, 44p666, 105p2325, 190p2348, 214p885, 666p678, 666p1647, 673p1145

ZC(X(3),L(3,6)):
3, 110, 250, 520

ZC(X(6),L(3,6)):
6, 110, 249, 512, 148p1101

ZC(X(101),L(3,6)):
101, 110, 662, 692, 31p932, 43p662

ZC(X(190),L(3,6)):
100, 110, 190, 662, 932, 43p662

ZC(X(512),L(3,6)):
100, 110, 190, 662, 932, 43p662

ZC(X(513),L(3,6)):
110, 513, 942, 1175, 1381, 1382, 28p1822, 28p1823, 523p1822, 523p1823

ZC(X(521),L(3,6)):
110, 521, 960, 1798, 21p1822, 21p1823, 523p1822, 523p1823

ZC(X(523),L(3,6)):
1, 5, 54, 110, 523, 1113, 1114, 9p1019, 523p1822, 523p1823

ZC(X(32),L(3,512)):
6, 25, 32, 511, 31p2065, 1755p2065, 1959p2065

ZC(X(39),L(3,512)):
2, 6, 39, 511, 38p2065, 1959p2065

ZC(X(2088),L(3,512)):
6, 323, 511, 525, 526, 2088, 74p661, 255p1300, 1959p2065

ZC(X(6),L(3,513)):
1, 6, 57, 517, 2323, 3p915, 57p2077, 63p915, 78p913, 915p1795

ZC(X(37),L(3,513)):
1, 2, 37, 2323, 63p915, 71p915, 72p915

ZC(X(109),L(3,517)):
101, 109, 651, 934, 100p2362, 109p366, 109p1489, 144p1461, 651p2067, 653p2066, 934p2066

ZC(X(112),L(3,517)):
108, 110, 112, 651, 63p1301, 101p229, 108p610

ZC(X(163),L(3,517)):
162, 163, 651, 662, 1415, 3p109, 99p2305, 163p1762, 1247p1415

ZC(X(222),L(3,517)):
222, 651, 905, 1262, 1262p1768

ZC(X(513),L(3,517)):
6, 7, 509, 513, 651, 100p2350

ZC(X(514),L(3,517)):
81, 174, 226, 514, 651, 2p1381, 2p1382, 514p1381, 514p1382

ZC(X(654),L(3,517)):
101, 104, 109, 651, 654, 2316, 2p654, 3p1845, 7p654, 44p1443, 57p102, 515p2323

ZC(X(665),L(3,517)):
101, 105, 109, 651, 665, 1362, 2254, 6p1280, 7p665, 7p911, 59p1566, 241p1279, 241p1381, 241p1382, 513p1381, 513p1382, 514p1381, 514p1382, 518p1381, 518p1382, 650p1381, 650p1382, 672p1381, 672p1382

ZC(X(668),L(3,517)):
190, 651, 664, 668, 2p932, 43p664, 99p171, 100p508, 190p978, 662p1999, 664p979

ZC(X(812),L(3,517)):
190, 651, 673, 812, 56p812, 190p978, 238p241

ZC(X(905),L(3,517)):
2, 222, 651, 905, 63p1381, 63p1382, 226p1822, 226p1823, 514p1381, 514p1382, 514p1822, 572p693

ZC(X(906),L(3,517)):
101, 109, 651, 906, 1331, 1813, 35p110, 46p1813, 90p101, 101p224, 906p1708

ZC(X(928),L(3,517)):
101, 109, 651, 928, 2p928, 7p928

ZC(X(1018),L(3,517)):
100, 190, 651, 1018, 9p1020, 10p1415, 100p1745, 190p978, 226p1293

ZC(X(1022),L(3,517)):
57, 88, 651, 1022, 2p901, 7p649

ZC(X(1024),L(3,517)):
6, 513, 651, 673, 1024, 2p919

ZC(X(1026),L(3,517)):
100, 651, 660, 664, 1025, 1026, 2284, 8p919, 43p664, 87p2284, 100p1743, 190p1477, 238p1025, 241p1025, 1025p2348

ZC(X(1415),L(3,517)):
101, 108, 109, 651, 1415, 1461, 3p109, 40p1461, 64p1813, 84p101, 108p610

ZC(X(1643),L(3,517)):
1, 6, 57, 513, 650, 651, 1643, 2246, 7p649, 7p2246, 44p2222, 56p528, 100p2246, 109p528, 514p840, 516p919, 517p2222, 528p1461, 1155p1308

ZC(X(2283),L(3,517)):
101, 109, 651, 927, 1025, 2283, 7p2283, 56p660, 101p1362, 238p1025

ZC(X(6),L(3,520)):
3, 6, 74, 1073, 3p2173, 3p2349, 20p2159, 74p2349

ZC(X(6),L(3,523)):
2, 4, 6, 30, 323, 19p2071, 48p1300, 63p1300, 255p1300

ZC(X(30),L(3,523)):
6, 13, 14, 30, 63p1300

ZC(X(190),L(4,6)):
100, 107, 190, 823, 932, 43p823, 100p1714

ZC(X(512),L(4,6)):
19, 107, 512, 800, 1379, 1380, 6p821, 19p1020, 19p1021

ZC(X(523),L(4,6)):
4, 107, 523, 1113, 1114, 162p1312

ZC(X(684),L(4,6)):
107, 110, 132, 684, 1297, 110p920, 158p684

ZC(X(112),L(4,8)):
100, 107, 112, 648, 1783, 2p1897, 112p502, 191p648

ZC(X(162),L(4,8)):
100, 162, 811, 823, 1783, 2p1897, 112p1330, 648p1654, 1897p2248

ZC(X(112),L(4,9)):
101, 107, 112, 648, 1897, 4p692, 112p1761, 162p1654, 1783p2248

ZC(X(1459),L(4,9)):
1, 109, 522, 1459, 1897, 27p836, 71p837, 109p1158

ZC(X(112),L(4,511)):
99, 107, 112, 648, 2p811, 22p162, 66p811, 159, 823, 162p1670, 162p1671, 811p1676, 811p1677

ZC(X(647),L(4,511)):
2, 110, 647, 850, 1899, 2p811, 157p662

ZC(X(4),L(4,512)):
4, 98, 232, 264, 2p158, 4p1821, 4p1910, 4p1966, 92p1687, 92p1688, 98p1956, 158p401

ZC(X(39),L(4,512)):
2, 4, 6, 39, 232, 248, 2p1733, 4p1821, 19p1235, 24p293, 38p98, 38p847, 311p1821, 427p1821, 427p1910

ZC(X(4),L(4,514)):
4, 281, 1861, 1886, 92p103, 103p273

ZC(X(10),L(4,514)):
2, 10, 75, 281, 1861, 2p1736, 92p103, 103p1441, 103p1826

ZC(X(516),L(4,514)):
7, 281, 516, 673, 1861, 92p103

ZC(X(112),L(4,515)):
107, 109, 112, 648, 653, 4p1415, 112p1762, 648p1046

ZC(X(163),L(4,515)):
109, 162, 163, 653, 662, 4p1415, 162p1781

ZC(X(112),L(4,516)):
101, 107, 112, 648, 1897, 4p692, 112p1761, 162p1654, 1783p2248

ZC(X(1459),L(4,516)):
1, 109, 522, 1459, 1897, 27p836, 71p837, 109p1158

ZC(X(3),L(4,523)):
3, 470, 471, 485, 486, 4p2349, 371p2349, 372p2349

ZC(X(4),L(4,523)):
4, 470, 471, 1990, 4p2349

ZC(X(6),L(4,523)):
2, 4, 6, 74, 186, 1990, 2p1725, 4p2159, 4p2349, 74p2166, 74p2349, 1138p2173, 1300p2159

ZC(X(30),L(4,523)):
13, 14, 30, 470, 471, 4p2349

ZC(X(140),L(4,523)):
17, 18, 140, 470, 471, 4p2349

ZC(X(440),L(4,523)):
226, 440, 470, 471, 1751, 4p2349, 950p2349

ZC(X(1865),L(4,523)):
4, 281, 445, 860, 1865, 1990, 2p225, 4p2349, 1859p2349, 1865p2349

ZC(X(512),L(5,6)):
216, 512, 925, 1379, 1380, 4p2168

ZC(X(523),L(5,6)):
3, 523, 847, 925, 1113, 1114

ZC(X(1),L(6,7)):
651, 658, 664, 927, 2283, 2p919, 6p927, 56p874, 292p927, 673p927

ZC(X(30),L(6,7)):
30, 514, 516, 927

ZC(X(190),L(6,7)):
100, 190, 664, 666, 927, 932, 2p927, 7p1025, 56p874, 85p1293, 190p1279, 192p927, 291p666, 294p666, 658p1376, 666p1743, 927p1280

ZC(X(511),L(6,7)):
511, 514, 516, 927

ZC(X(512),L(6,7)):
512, 514, 516, 927, 1379, 1380, 65p919

ZC(X(513),L(6,7)):
241, 513, 514, 516, 927, 1381, 1382, 2p919, 2p1381, 2p1382, 6p927, 7p513, 7p1279, 7p1381, 7p1382, 105p673, 105p1280, 105p1280, 885p1381, 885p1382

ZC(X(522),L(6,7)):
514, 516, 522, 666, 927, 666p1743, 1111p1293

ZC(X(523),L(6,7)):
514, 516, 523, 693, 857, 927, 1113, 1114, 37p927, 42p927, 226p1113, 226p1114

ZC(X(526),L(6,7)):
74, 110, 514, 516, 526, 927, 1442, 35p885, 105p758, 500p673, 658p2245

ZC(X(651),L(6,7)):
651, 658, 664, 927, 2283, 2p919, 6p927, 56p874, 292p927, 673p927

ZC(X(659),L(6,7)):
57, 100, 105, 659, 927, 1447, 2p1027, 58p693, 59p812, 105p239, 190p1279, 812p1462

ZC(X(676),L(6,7)):
2, 105, 108, 676, 927, 2p1027, 7p513, 7p516, 7p1279, 190p1456, 516p1462, 666p910

ZC(X(684),L(6,7)):
110, 684, 693, 927, 1214, 1297, 105p1959, 108p1959, 520p673, 1814p2294

ZC(X(804),L(6,7)):
98, 99, 514, 516, 804, 927, 7p171, 105p740, 171p885, 239p1020, 740p961

ZC(X(900),L(6,7)):
7, 100, 104, 514, 516, 655, 673, 885, 900, 927, 2p1022, 2p1319, 7p2254, 44p658, 44p673, 44p927, 190p1279, 678p927, 927p1647

ZC(X(918),L(6,7)):
508, 514, 516, 664, 918, 927, 7p876, 56p874, 85p103

ZC(X(926),L(6,7)):
1, 101, 103, 514, 516, 926, 927, 7p2283, 8p884, 105p1212, 241p2346

ZC(X(1633),L(6,7)):
100, 653, 927, 934, 1633, 2p919, 2p1633, 6p927, 7p1292, 7p1633, 112p857, 190p1279, 516p934, 614p883, 614p927, 666p1438, 666p1473, 666p2082

ZC(X(2284),L(6,7)):
101, 664, 813, 927, 2284, 56p874, 100p509

ZC(X(2284),L(6,8)):
101, 190, 813, 2284, 99p2295, 100p1220, 572p1018, 1026p1220, 2284p2298

ZC(X(101),L(6,10)):
101, 190, 835, 1897, 31p835, 48p835, 100p1011, 835p2282

ZC(X(190),L(6,10)):
101, 190, 835, 932, 2p835, 100p1698, 192p835

ZC(X(190),L(6,11)):
100, 190, 929, 932, 2p929, 192p929

ZC(X(351),L(6,13)):
110, 111, 351, 476, 110p1749, 351p2166

ZC(X(511),L(6,13)):
30, 476, 511, 523

ZC(X(512),L(6,13)):
30, 476, 512, 523, 1379, 1380, 4p661, 4p2315, 31p476, 48p476, 393p2314, 1989p2159

ZC(X(523),L(6,13)):
30, 476, 523, 1113, 1114, 74p2166

ZC(X(526),L(6,13)) ( = Z(X(476),X(1)), [Tixier cubic, K130]:
1, 30, 74, 110, 476, 523, 526, 110p1749, 1109p1291

ZC(X(690),L(6,13)):
13, 14, 30, 476, 523, 690, 13p896, 14p896, 111p1577, 395p662, 396p662, 476p896

ZC(X(804),L(6,13)):
30, 98, 99, 476, 523, 804, 79p171, 80p238, 476p1580

ZC(X(826),L(6,13)):
30, 476, 523, 826, 850, 38p476, 476p1964

ZC(X(900),L(6,13)):
30, 79, 100, 104, 476, 523, 900, 476p1647, 514p2341, 519p759, 553p2341

ZC(X(926),L(6,13)):
30, 101, 103, 476, 523, 926, 9p2160, 79p2283, 241p2341, 650p2341, 942p2341

ZC(X(1),L(30,511)) ( = Z(X(2),X(6)):
1, 2, 7, 9, 366, 1489, 2p1419, 2p2067, 7p2066, 8p2362, 92p2066, 173p1489, 364p366

ZC(X(3),L(30,511)) ( = Z(X(2),X(19)):
2, 3, 6, 69, 485, 486, 2p2066, 2p2067, 7p2066, 8p2067, 48p491, 48p492

ZC(X(6),L(30,511)):
1, 2, 3, 4, 6, 9, 57, 223, 282, 1073, 1249, 1249, 84p1490, 204p1032, 221p1034, 1073p1712, the Thomson cubic.

ZC(X(9),L(30,511)) ( = Z(X(2),X(56)):
1, 2, 8, 9, 188, 236, 8p289, 8p1743, 514p1293

ZC(X(10),L(30,511)):
2, 10, 37, 75, 2p192, 10p2162

ZC(X(11),L(30,511)):
2, 11, 650, 693, 8p2350, 508p650, 1111p1621

ZC(X(15),L(30,511)):
2, 3, 6, 13, 15, 18, 298, 470, 1082, 2p1094,2p1250, 15p1081, 16p2349, 61p2167, 283p1832, 303p2151, 533p2154, 621p2151

ZC(X(16),L(30,511)):
2, 3, 6, 14, 16, 17, 299, 471, 559, 2p1095, 9p559, 15p2349, 16p554, 62p2167, 283p1833, 302p2152, 532p2153, 617p2154, 622p2152

ZC(X(23),L(30,511)):
2, 23, 111, 251, 23p1930, 316p896

ZC(X(30),L(30,511)):
2, 13, 14, 30, 1494, 6p1099, 298p2173, 299p2173, 617p2154

ZC(X(32),L(30,511)) ( = Z(X(2),X(75)):
2, 3, 6, 25, 32, 66, 206, 1676, 1677, 19p159, 31p1670, 31p1671

ZC(X(37),L(30,511)) ( = Z(X(2),X(58)):
1, 2, 9, 10, 37, 226, 281, 1214, 2p2331, 10p1433, 20p1903, 40p2184, 1490p2184

ZC(X(39),L(30,511)) ( - Z(X(2),X(82)):
2, 3, 6, 39, 141, 427, 38p1342, 38p1343, 63p66, 427p2172, 1370p2156

ZC(X(44),L(30,511)) ( = Z(X(2),X(106)):
1, 2, 9, 44, 80, 88, 214, 519, 2p678, 2p1319, 2p2342, 57p1145

ZC(X(45),L(30,511)):
1, 2, 9, 45, 1000, 2p45, 2p2099, 44p80, 80p517

ZC(X(50),L(30,511)):
2, 3, 6, 50, 186, 323, 323p1749, 661p1291

ZC(X(52),L(30,511)):
2, 3, 6, 52, 467, 47p311

ZC(X(53),L(30,511)):
2, 4, 5, 53, 216, 1249, 2p158, 5p2184, 92p1075

ZC(X(56),L(30,511)) ( = Z(X(2),X(9)):
2, 56, 478, 509, 2362, 2p2067, 7p2066, 225p1806

ZC(X(57),L(30,511)) ( = Z(X(2),X(55)):
2, 57, 174, 189, 223, 557, 558, 1659, 2p2067, 7p2066, 57p175, 57p176, 164p174, 174p505, 273p2066

ZC(X(58),L(30,511)) ( = Z(X(2),X(37)):
2, 3, 6, 27, 58, 86, 2248, 81p1654

ZC(X(61),L(30,511)):
2, 3, 6, 61, 302, 473

ZC(X(62),L(30,511)):
2, 3, 6, 62, 303, 472

ZC(X(72),L(30,511)):
1, 2, 9, 72, 306, 307, 2p1751, 63p209, 306p1724, 307p1754

ZC(X(115),L(30,511)):
2, 115, 523, 1312, 1313, 338p1822, 338p1823, 661p1113, 661p1114, 1109p1379, 1109p1380, 1379p1577, 1380p1577

ZC(X(173),L(30,511)):
2, 173, 174, 188, 236, 2089, 164p174, 168p2089, 177p1128, 236p505

ZC(X(173),L(30,511)):
2, 3, 6, 182, 183, 458, 98p1966, 290, 1955

ZC(X(187),L(30,511)) [Droussent medial cubic, K043] :
2, 3, 6, 67, 111, 187, 468, 524, 1560, 9p1366, 23p896, 63p1177

ZC(X(213),L(30,511)) ( = Z(X(2),X(86)):
1, 2, 9, 42, 213, 1400, 1400p1764

ZC(X(216),L(30,511)):
2, 3, 5, 6, 216, 343, 2165, 47p343, 52p921, 68p920

ZC(X(219),L(30,511)) ( = Z(X(2),X(34)):
1, 2, 9, 63, 78, 219, 8p2164, 9p224, 12p1789, 21p35, 46p63, 72p1780

ZC(X(238),L(30,511)):
1, 2, 9, 86, 238, 239, 292, 673, 893, 1447, 1929, 1966, 2238, 6p1281, 81p1654, 238p350, 238p518, 239p1757, 335p2112, 366p2068, 366p2069, 673p1282, 740p2248

ZC(X(269),L(30,511)):
2, 7, 57, 223, 269, 1440, 2p1419, 7p365

ZC(X(284),L(30,511)) ( - Z(X(2),X(65)):
2, 3, 6, 29, 284, 333, 6p1247, 284p1762, 314p2305

ZC(X(371),L(30,511)):
2, 3, 6, 371, 492, 1585

ZC(X(372),L(30,511)):
2, 3, 6, 372, 1586

ZC(X(393),L(30,511)):
2, 4, 278, 281, 393, 1249, 2p207, 2p2331, 4p84, 4p1712, 4p2184, 19p1032, 19p1034

ZC(X(397),L(30,511)):
2, 4, 17, 397, 465, 1249, 465p2184

ZC(X(398),L(30,511)):
2, 4, 18, 398, 466, 1249, 466p2184

ZC(X(440),L(30,511)):
2, 226, 306, 440, 1214, 1751, 2p950, 2p1104, 21p440, 306p1724

ZC(X(511),L(30,511)):
2, 3, 6, 290, 297, 325, 511, 694, 2009, 2010, 3p1956, 9p1355, 237p1926, 240p401, 1687p1959, 1688p1959

ZC(X(513),L(30,511)):
2, 513, 668, 1015, 1978p1979

ZC(X(514),L(30,511)):
2, 190, 514, 1086, 190p1054

ZC(X(516),L(30,511)):
2, 7, 516, 673, 2p1419, 8p910, 9p1360, 75p103, 516p518, 673p1282

ZC(X(518),L(30,511)):
1, 2, 9, 291, 518, 2p241, 2p518, 2p673, 9p1362, 239p518, 335p2110

ZC(X(523),L(30,511)):
2, 99, 115, 523, 148p662

ZC(X(532),L(30,511)):
2, 299, 396, 532, 618, 94p1095

ZC(X(533),L(30,511)):
2, 298, 395, 533, 619, 94p1094

ZC(X(570),L(30,511)):
2, 3, 6, 54, 570, 1209, 1594, 19p1238, 48p93

ZC(X(571),L(30,511)):
2, 3, 6, 24, 70, 571, 1993, 26p47, 49p2190

ZC(X(577),L(30,511)):
2, 3, 6, 68, 394, 577, 1147, 9p921, 63p155, 547p1820

ZC(X(594),L(30,511)):
2, 10, 37, 321, 594, 596, 595p1089

ZC(X(698),L(30,511)):
2, 76, 698, 1916, 6p2227, 75p194, 75p699, 385p2227, 698p2227

ZC(X(726),L(30,511)):
2, 75, 335, 726, 1575, 2p192, 75p727, 87p1575, 238p726, 335p2108, 726p1575

ZC(X(732),L(30,511)):
2, 39, 141, 385, 732, 2p1966, 75p733, 732p2236, 1966p2076

ZC(X(740),L(30,511)):
2, 10, 37, 239, 350, 740, 2p2107, 10p1929, 28p337, 239p1757, 740p2238

ZC(X(960),L(30,511)):
1, 2, 9, 314, 960, 2092, 2p960, 7p960, 8p893, 69p444, 256p1045, 960p1999

ZC(X(984),L(30,511)):
1, 2, 9, 75, 984, 2276, 2p192, 2p984, 2p1002, 7p984, 10p893, 87p2276, 291p518, 291p1575, 984p1001

ZC(X(984),L(30,511)):
1, 2, 9, 79, 81, 553, 110, 1125, 1213, 2p501, 35p1125, 267p1213

ZC(X(1104),L(30,511)):
1, 2, 9, 28, 440, 1104, 2p1104, 7p1104

ZC(X(1107),L(30,511)):
1, 2, 9, 256, 274, 1107, 2p1107, 7p1107, 10p1197, 86p1655, 894p1107

ZC(X(1108),L(30,511)):
1, 2, 9, 84, 278, 1108, 1210, 2p207, 7p1108, 40p1210, 63p1864

ZC(X(1147),L(30,511)):
2, 317, 371, 372, 577, 1147, 48p491, 48p492

ZC(X(1212),L(30,511)):
1, 2, 9, 142, 277, 1212, 2p1212, 344p2293

ZC(X(1333),L(30,511)):
2, 3, 6, 28, 81, 1333, 2p501, 6p267

ZC(X(1418),L(30,511)):
2, 57, 142, 223, 279, 1212, 1418, 7p2124, 84p142, 354p2125

ZC(X(1427),L(30,511)):
2, 57, 223, 226, 278, 1214, 1427, 2184, 2p207, 7p1903, 20p1427, 208p1032

ZC(X(1465),L(30,511)):
2, 57, 223, 908, 1465, 2006, 2p102, 36p908, 84p908, 515p1465

ZC(X(1503),L(30,511)):
2, 4, 98, 441, 1249, 1503, 63p132, 75p1297, 147p1910, 441p2184, 1503p2312

ZC(X(1513),L(30,511)):
2, 98, 132, 232, 262, 325, 1513, 147p1910, 237p1926, 336p1513, 1513p1910, 1513p1959

ZC(X(1691),L(30,511)):
2, 3, 6, 83, 98, 171, 238, 385, 419, 1429, 1691, 2329, 2p1927, 6p1281, 6p2236, 31p695, 147p1910, 237p1966, 384p1966, 385p1966, 1966p2076

ZC(X(1692),L(30,511)):
2, 3, 6, 114, 230, 460, 1692, 1976

ZC(X(1834),L(30,511)):
2, 4, 10, 37, 440, 1249, 1834, 2p1104, 2p1427, 7p950, 8p2264, 440p2184

ZC(X(1901),L(30,511)):
2, 4, 226, 1214, 1249, 1901, 2p1903, 21p1901, 29p1901, 63p1901, 1817p1901

ZC(X(1921),L(30,511)):
2, 75, 274, 334, 350, 1921, 1966, 2p192, 2p257, 2p740, 8p673, 75p2068, 75p2069, 76p727, 86p1655, 87p350, 238p350, 239p726, 241p350, 310p2107

ZC(X(1990),L(30,511)):
2, 4, 30, 133, 1249, 1294, 1990, 4p2349, 6p1099, 30p2184

ZC(X(2088),L(30,511)):
2, 3, 6, 2088, 74p661, 75p2088, 92p2088, 129p371, 526p1725, 656p1300, 1109p1379, 1109p1380, 1511p1577

ZC(X(2092),L(30,511)):
2, 3, 6, 10, 37, 65, 429, 960, 1193, 1211, 2092, 2p1193, 65p573, 197p1848, 572p2292

ZC(X(2176),L(30,511)) ( = Z(X(2),X(87)):
1, 2, 9, 43, 1423, 2176, 37p904

ZC(X(2193),L(30,511)):
2, 3, 6, 21, 1812, 2193, 9p229

ZC(X(2207),L(30,511)):
2, 4, 19, 25, 1249, 1435, 2207, 4p220, 4p2155, 19p159, 19p1763, 19p2138, 19p2139

ZC(X(2256),L(30,511)):
1, 2, 9, 268, 936, 2256, 2p939, 2p1466, 196p936, 268p1767, 936p2257

ZC(X(2284),L(30,511)):
1, 2, 9, 1025, 1026, 2284

ZC(X(2321),L(30,511)):
2, 8, 10, 37, 312, 2321, 8p1743, 37p979, 312p978, 1293p1577

ZC(X(851),L(44,513)):
1, 65, 73, 243, 851, 1936, 2p2249, 851p851

ZC(X(910),L(44,513)):
1, 57, 105, 910, 1419, 2p103, 9p910, 55p1360, 59p1566, 105p1282

ZC(X(922),L(44,513)):
1, 31, 48, 896, 922, 923, 2157, 3p1177, 4p187, 6p1560, 23p187, 55p1366

ZC(X(1418),L(44,513)):
1, 57, 279, 354, 1418, 1419, 2293, 170p279

ZC(X(1457),L(44,513)):
1, 56, 102, 221, 517, 1411, 1457, 3p1845, 84p517, 515p1457

ZC(X(1464),L(44,513)):
1, 36, 65, 73, 74, 1464, 1870, 3p1832, 3p1833, 15p2306, 30p1464, 36p484, 554p2152

ZC(X(1575),L(44,513)):
1, 2, 192, 291, 1575, 2p727, 6p1575, 238p1575, 291p2108, 1463p2053, 1575p1575

ZC(X(1864),L(44,513)):
1, 4, 9, 1108, 1148, 1864, 3p1864, 9p1743

ZC(X(1905),L(44,513)):
1, 4, 1061, 1064, 1148, 1905, 1060p1905

ZC(X(1962),L(44,513)):
1, 37, 42, 1100, 1125, 1962, 31p596, 1230p2220

ZC(X(2151),L(44,513)):
1, 31, 48, 1094, 1250, 2151, 2153, 2307, 2p15, 4p15, 6p18, 15p62, 15p1251, 15p2306, 16p74, 54p61, 1250p1653

ZC(X(2173),L(44,513)):
1, 2153, 2154, 2173, 2349, 13p1511, 14p1511, 30p1495

ZC(X(2181),L(44,513)):
1, 19, 158, 204, 1953, 2181, 2p217, 4p1075, 5p64

ZC(X(2227),L(44,513)):
1, 75, 1581, 2227, 2p194, 2p699, 31p2227, 698p1691, 2227p2227

ZC(X(2236),L(44,513)):
1, 38, 1580, 1964, 2236, 2p733, 69p419, 385p2076, 2236p2236

ZC(X(2238),L(44,513)):
1, 37, 42, 238, 239, 2107, 2238, 2p741, 2p2054, 238p1757, 740p2106, 2238p2238

ZC(X(2268),L(44,513)):
1, 6, 55, 940, 958, 2268, 2339, 21p894, 21p1999, 612p1468

ZC(X(2276),L(44,513)):
1, 2, 6, 55, 192, 869, 984, 1002, 2276, 2p1469, 10p904, 87p869, 291p672, 292p1575, 984p2280, 1282p2113, 2108p2113

ZC(X(2293),L(44,513)):
1, 6, 55, 354, 1212, 2293, 218p1212, 513p1292

ZC(X(2309),L(44,513)):
1, 6, 55, 86, 893, 1107, 2309, 7p2309, 37p1197, 81p1655, 171p1107

ZC(X(2312),L(44,513)):
1, 19, 204, 1910, 2312, 2p1297, 3p132, 3p1503, 64p441, 147p1976, 2312p2312

ZC(X(2313),L(44,513)):
1, 1953, 1955, 2313, 2p217, 2p1298, 4p401, 2313p2313

ZC(X(2348),L(44,513)):
1, 9, 294, 1279, 2348, 2p1477, 9p1743, 241p2348, 2348p2348

ZC(X(2361),L(44,513)):
1, 6, 36, 55, 2323, 2361, 36p484, 650p1290,


B(U,P): Bicentrics Collinearity Cubics

ux(qryz - p2x2) + vy(rpzx - q2y2) + wz(pqxy - r2z2) = 0

B(X(1),X(8)):
6, 56, 649, 1458, 513p1381, 513p1382

B(X(1),X(58)):
10, 37, 661, 740

B(X(1),X(513)):
513, 514, 650, 812, 2254, 43p514, 513p1575, 514p1742

B(X(2),X(43)):
1, 87, 649, 1463p2053

B(X(2),X(81)):
37, 42, 512, 2238

B(X(2),X(100)):
513, 649, 663, 665, 43p513, 513p1742, 649p1575

B(X(2),X(107)):
520, 647, 684, 20p810, 193p822, 230p822, 441p810

B(X(2),X(110)):
512, 523, 647, 804, 19p684, 194p661, 401p661, 512p2227

B(X(3),X(4)):
3, 6, 511, 647, 523p1822, 523p1823

B(X(3),X(29)):
65, 73, 647, 851

B(X(3),X(78)):
19, 34, 1876, 4p649

B(X(4),X(20)):
6, 64, 647, 441p2155

B(X(4),X(21)):
65, 73, 647, 851

B(X(4),X(28)):
71, 72, 647, 3p740

B(X(4),X(76)):
32, 184, 237, 3p798, 512p1822, 512p1823

B(X(4),X(112)):
520, 525, 647, 684, 63p804, 194p656, 401p656, 647p2227

B(X(5),X(3)):
4, 6, 647, 4p1955

B(X(6),X(9)):
1, 57, 241, 513, 514p1381, 514p1382

B(X(6),X(69)):
6, 25, 232, 512, 661p1113, 661p1114

B(X(7),X(75)):
31, 41, 2223, 6p663, 663p1381, 663p1382

B(X(8),X(85)):
31, 41, 2223, 6p663, 663p1381, 663p1382

B(X(9),X(7)):
6, 55, 663, 672, 650p1381, 650p1382

B(X(10),X(1)):
1, 6, 238, 649

B(X(10),X(76)):
31, 32, 1919, 2210

B(X(10),X(78)):
34, 56, 649, 1430

B(X(10),X(99)):
512, 649, 798, 42p659, 423p810, 512p2106, 649p846, 649p1045

B(X(10),X(101)):
514, 649, 1459, 28p684, 81p804, 194p513, 401p513, 649p2227

B(X(19),X(75)):
31, 48, 810, 1755, 647p1113, 647p1114

B(X(25),X(2)):
3, 6, 511, 647, 523p1822, 523p1823

B(X(25),X(27)):
71, 72, 647, 3p740

B(X(28),X(29)):
71, 73, 647, 65p1818, 656p1381, 656p1382

B(X(31),X(55)):
71, 73, 647, 65p1818, 656p1381, 656p1382

B(X(31),X(63)):
1, 19, 240, 661, 523p1113, 523p1114

B(X(31),X(100)):
513, 514, 650, 812, 2254, 43p514, 513p1575, 514p1742

B(X(32),X(3)):
2, 4, 297, 523, 1113p1577, 1114p1577

B(X(32),X(99)):
512, 523, 647, 804, 19p684, 194p661, 401p661, 512p2227

B(X(32),X(101)):
514, 522, 693, 918, 2p812, 43p693, 513p726, 693p1742

B(X(42),X(110)):
514, 523, 661, 10p659, 423p656, 513p1654, 513p1655, 523p2106

B(X(55),X(57)):
1, 9, 518, 650, 522p1381, 522p1382

B(X(55),X(109)):
514, 522, 918, 9p676, 144p513, 145p650, 514p2348

B(X(56),X(1)):
1, 9, 518, 650, 522p1381, 522p1382

B(X(56),X(101)):
514, 522, 918, 9p676, 144p513, 145p650, 514p2348

B(X(57),X(2)):
6, 55, 663, 672, 650p1381, 650p1382

B(X(57),X(100)):
513, 650, 2254, 55p676, 144p649, 145p663, 513p2348

B(X(58),X(101)):
514, 523, 661, 10p659, 423p656, 513p1654, 513p1655, 523p2106

B(X(81),X(100)):
514, 523, 661, 10p659, 423p656, 513p1654, 513p1655, 523p2106

B(X(105),X(100)):
513, 650, 665, 2254, 109p1566, 238p2254, 513p1282, 514p2110

B(X(109),X(100)):
513, 650, 2170, 2254, 11p1381, 11p1382

B(X(110),X(107)):
520, 647, 684, 41p1367, 125p1822, 125p1823

B(X(114),X(98)):
3, 6, 511, 19p684

B(X(125),X(110)):
6, 523, 1316, 19p684

B(X(132),X(98)):
3, 6, 511, 511p656

B(X(141),X(6)):
2, 6, 385, 512

B(X(184),X(2)):
6, 523, 1316, 19p684

B(X(184),X(25)):
2, 69, 325, 525, 850p1822, 850,1823

B(X(184),X(107)):
520, 525, 647, 684, 63p804, 194p656, 401p656, 647p2227

B(X(200),X(2)):
6, 56, 649, 1458, 513p1381, 513p1382

B(X(213),X(1)):
1, 2, 239, 513

B(X(213),X(32)):
75, 76, 693, 1921

B(X(213),X(72)):
28, 81, 513, 27p511, 514p1113, 514p1114

B(X(217),X(3)):
4, 470, 471, 458p661

B(X(217),X(4)):
2, 3, 401, 520

B(X(220),X(1)):
1, 57, 241, 513, 514p1381, 514p1382

B(X(225),X(1)):
1, 3, 652, 1936

B(X(226),X(99)):
512, 663, 810, 243p810, 415p810, 416p512, 650p2305, 663p1047

B(X(226),X(109)):
522, 652, 663, 21p804, 194p650, 232p521, 401p650, 663p2227

B(X(235),X(3)):
3, 4, 450, 647

B(X(244),X(11)):
59, 101, 1252, 59p518, 100p1381, 100p1382

B(X(244),X(88)):
44, 1023, 1635, 1023p1052, 1023p1054

B(X(255),X(1)):
1, 19, 240, 661, 523p1113, 523p1114

B(X(284),X(109)):
522, 523, 656, 243p656, 415p656, 416p523, 522p1046, 522p1047

B(X(287),X(107)):
520, 647, 684, 31p684, 132p822, 147p810, 684p1580

B(X(291),X(100)):
513, 649, 659, 37p659, 513p2108, 659p1575, 659p1757

B(X(291),X(101)):
513, 514, 812, 37p659, 238p2254, 514p2110

B(X(292),X(101)):
513, 514, 812, 10p659, 514p2108, 659p726, 812p1757

B(X(326),X(75)):
31, 798, 1973, 2p2211, 512p1113, 512p1114

B(X(335),X(100)):
513, 649, 659, 42p659, 238p665, 513p2110

B(X(341),X(76)):
32, 1397, 1919, 31p1458, 667p1381, 667p1382

B(X(346),X(75)):
31, 604, 667, 6p1458, 649p1381, 649p1382

B(X(394),X(2)):
6, 25, 232, 512, 661p1113, 661p1114

B(X(512),X(2)):
6, 15, 16, 6p2234

B(X(512),X(3)):
2, 4, 193, 230, 297, 1249, 1503

B(X(512),X(10)):
58, 81, 284, 21p1423, 21p1458, 58p1575, 81p1742

B(X(512),X(15)):
2, 13, 30, 395, 94p1095

B(X(512),X(16)):
2, 14, 30, 396, 94p1094, 617p2154

B(X(512),X(32)):
2, 69, 76, 325, 698, 2p1966, 75p194, 75p401

B(X(512),X(58)):
2, 10, 37, 740, 1654, 1655, 2p1757, 10p2106

B(X(512),X(76)):
6, 32, 184, 237, 1613, 1691, 1971, 32p2227

B(X(513),X(6)):
1, 2, 9, 192, 239, 518, 1575, 2p1742

B(X(513),X(9)):
1, 57, 241, 910, 1279, 1419, 1743

B(X(513),X(37)):
1, 6, 81, 238, 1931, 2106, 58p1654, 58p1655

B(X(513),X(75)):
6, 31, 41, 1914, 2176, 2223, 6p1742, 31p1575

B(X(514),X(1)):
1, 6, 43, 55, 238, 672, 1742, 6p1575

B(X(514),X(8)):
6, 56, 1458, 6p910, 6p1279, 6p1419, 6p1743

B(X(514),X(10)):
6, 31, 58, 1326, 1914, 6p2106, 58p846, 58p1045

B(X(514),X(58)):
10, 42, 71, 10p1580, 10p1740, 10p1755, 10p1955, 42p2227

B(X(514),X(76)):
31, 32, 2175, 2209, 2210, 6p2223, 31p1742, 32p1575

B(X(520),X(6)):
2, 4, 193, 230, 297, 1249, 1503

B(X(522),X(7)):
6, 55, 672, 6p2348, 41p145, 41p516

B(X(522),X(9)):
6, 56, 57, 1423, 1429, 1458, 6p1463, 57p1742

B(X(522),X(63)):
6, 19, 2178, 2202, 6p1148

B(X(523),X(3)):
6, 19, 2178, 2202, 6p1148

B(X(523),X(6)):
2, 3, 6, 194, 385, 401, 511, 6p2227

B(X(523),X(30)):
6, 15, 16, 74, 617p2159

B(X(523),X(37)):
58, 81, 284, 21p1423, 21p1429, 21p1458, 58p1575, 81p1742

B(X(523),X(69)):
6, 25, 232, 1692, 6p204, 6p1707, 6p2312

B(X(523),X(86)):
1, 42, 213, 3p862, 6p846, 6p1045, 6p1757, 42p2106

B(X(525),X(3)):
4, 6, 25, 232, 419, 4p1740, 4p1955, 25p2227

B(X(525),X(4)):
3, 6, 154, 511, 3p1707, 3p2312, 48p230

B(X(525),X(72)):
28, 1474, 2299, 27p1914, 27p2176, 27p2223, 28p1742, 726p2203

B(X(526),X(50)):
94, 265, 1989, 94p1580, 94p1740, 94p1755, 94p1955, 1989p2227

B(X(560),X(48)):
75, 92, 1577, 2p297, 850p1113, 850p1114

B(X(647),X(25)):
2, 20, 69, 325, 441, 3p1733, 63p193

B(X(649),X(2)):
1, 6, 43, 55, 238, 672, 1742, 6p1575

B(X(649),X(31)):
2, 8, 75, 350, 726, 2p192, 2p518, 75p1742

B(X(649),X(42)):
1, 2, 86, 239, 2p1931, 2p2106, 81p1654, 81p1655

B(X(649),X(55)):
2, 7, 145, 516, 2p241, 2p1279, 2p1419

B(X(649),X(60)):
10, 12, 10p851, 10p1046, 10p1047, 10p1758, 12p416, 37p1214

B(X(650),X(3)):
1, 4, 46, 243, 1148

B(X(650),X(55)):
1, 7, 57, 241, 1447, 1463, 2p1423, 7p1742

B(X(650),X(57)):
1, 9, 165, 518, 2348, 9p910, 9p1743

B(X(650),X(65)):
1, 3, 21, 416, 1936, 3p415, 21p1046, 21p1047

B(X(651),X(59)):
11, 2170, 2310, 11p43, 11p238, 22p672, 11p1742, 1463p2310

B(X(652),X(73)):
1, 4, 29, 243, 415, 4p416, 29p1046, 29p1047

B(X(656),X(19)):
1, 63, 610, 1959, 3p193, 3p230, 3p1503

B(X(656),X(48)):
1, 19, 92, 240, 2p419, 4p194, 4p401, 19p2227

B(X(656),X(71)):
27, 28, 1172, 21p1876, 27p43, 27p238, 27p1742, 28p1575

B(X(657),X(6)):
2, 7, 145, 516, 2p241, 2p1279, 2p1419

B(X(657),X(7)):
1, 6, 43, 55, 238, 672, 1742, 6p1575

B(X(657),X(42)):
7, 77, 86, 416, 7p1936, 77p415, 86p1046, 86p1047

B(X(661),X(21)):
1, 65, 73, 851, 1046, 1047, 1758, 65p416

B(X(661),X(42)):
21, 81, 86, 21p241, 21p1447, 21p1463, 43p86, 86p1742

B(X(661),X(63)):
1, 19, 204, 240, 1707, 2312, 2p1692

B(X(661),X(81)):
1, 37, 42, 846, 1045, 1757, 2238, 37p2106

B(X(663),X(8)):
6, 56, 57, 1423, 1429, 1458, 6p1463, 57p1742

B(X(663),X(41)):
2, 7, 85, 2p241, 2p1447, 2p1463, 7p192, 85p1742

B(X(663),X(56)):
2, 8, 144, 2p518, 2p2348, 8p910, 8p1743

B(X(663),X(60)):
12, 226, 2171, 10p1284, 12p1931, 12p2106, 65p1654, 65p1655

B(X(667),X(1)):
1, 2, 9, 192, 239, 518, 1575, 2p1742

B(X(667),X(32)):
75, 76, 312, 1921, 2p726, 43p76, 69p1861, 76p1742

B(X(669),X(2)):
2, 3, 6, 194, 385, 401, 511, 6p2227

B(X(669),X(42)):
86, 274, 333, 43p274, 81p726, 86p518, 274p1742

B(X(669),X(50)):
94, 300, 301, 75p395, 75p396

B(X(669),X(81)):
2, 10, 37, 740, 1654, 1655, 2p1757, 10p2106

B(X(693),X(2)):
6, 31, 41, 1914, 2176, 2223, 6p1742, 31p1575

B(X(693),X(81)):
37, 213, 228, 10p237, 10p1613, 10p1691, 10p1971, 213p2227

B(X(798),X(37)):
21, 81, 86, 21p241, 21p1447, 21p1463, 43p86, 86p1742

B(X(798),X(37)):
1, 31, 48, 1580, 1740, 1755, 1955, 31p2227

B(X(798),X(86)):
1, 37, 42, 846, 1045, 1757, 2238, 37p2106

B(X(810),X(72)):
27, 28, 1172, 21p1876, 27p43, 27p238, 27p1742, 28p1575

B(X(822),X(29)):
1, 65, 73, 851, 1046, 1047, 1758, 65p416

B(X(822),X(31)):
75, 92, 1733, 1895, 2p193, 2p297, 2p1503

B(X(822),X(92)):
1, 31, 1580, 1740, 1755, 1955, 31p2227, 34p2289

B(X(826),X(39)):
83, 251, 1176, 82p194, 82p385, 82p401, 82p511, 251p2227

B(X(850),X(2)):
6, 32, 184, 237, 1613, 1691, 1971, 32p2227

B(X(875),X(1)):
1, 2, 239, 2238, 2p2110, 238p518, 740p2106

B(X(875),X(2)):
1, 6, 238, 2108, 2238, 238p1575, 238p1757

B(X(875),X(31)):
2, 75, 350, 2p740, 75p2108, 239p726, 350p1757

B(X(876),X(1)):
1, 6, 238, 2108, 2238, 238p1575, 238p1757

B(X(876),X(6)):
1, 2, 239, 2238, 2p2110, 238p518, 740p2106

B(X(876),X(76)):
31, 32, 2210, 31p2108, 31p2238, 1575p2210, 1757, 2210

B(X(878),X(3)):
2, 4, 132, 232, 297, 19p147, 232p1966

B(X(879),X(69)):
6, 25, 232, 2211, 21p132, 147p1973, 232p1580

B(X(884),X(55)):
2, 7, 241, 2p241, 2p2114, 85p2110, 239p241, 241p516

B(X(885),X(8)):
6, 56, 1458, 6p1458, 57p2110, 238p1458, 672p1456

B(X(900),X(44)):
88, 106, 2316, 43p88, 88p238, 88p672, 88p1742, 106p1575

B(X(905),X(78)):
19, 34, 1876, 6p1886, 19p1279, 19p1419, 19p1743

B(X(1019),X(1)):
1, 37, 42, 846, 1045, 1757, 2238, 37p2106

B(X(1019),X(58)):
10, 37, 210, 740, 10p43, 10p672, 10p1742, 37p1575

B(X(1021),X(1)):
1, 65, 73, 851, 1046, 1047, 1758, 65p416

B(X(1024),X(9)):
1, 57, 241, 1458, 2114, 7p2110, 238p241, 241p910

B(X(1027),X(1)):
1, 9, 518, 672, 1282, 2p2110, 59p1566, 238p518

B(X(1459),X(69)):
19, 25, 607, 2201, 2356, 4p2176, 19p1742, 25p1575

B(X(1459),X(71)):
4, 19, 27, 242, 423, 4p2106, 27p1045

B(X(1577),X(71)):
1, 31, 48, 1580, 1740, 1755, 1955, 31p2227

B(X(1635),X(100)):
1, 244, 513, 1052, 1054

B(X(1919),X(6)):
2, 8, 75, 350, 726, 2p192, 2p518, 75p1742

B(X(1924),X(1)):
1, 63, 75, 1959, 2227, 2p194, 2p401 83p732

B(X(2254),X(105)):
1, 9, 518, 672, 1282, 2p2110, 59p1566, 238p518


BP(U,P): B-Plus Cubics

ux(qryz + p2x2) + vy(rpzx + q2y2) + wz(pqxy + r2z2) = 0

BP(X(1),X(88)):
1, 44

BP(X(1),X(100)):
513, 1635

BP(X(2),X(99)):
513, 1635

BP(X(2),X(670)):
669, 887, 15p798, 16p798

BP(X(2),X(671)):
187, 351

BP(X(3),X(110)):
523, 1637

BP(X(4),X(107)):
520, 1636

BP(X(6),X(99)):
512, 888, 15p661, 16p661

BP(X(6),X(100)):
513, 891

BP(X(6),X(101)):
514, 900

BP(X(6),X(106)):
519,900

BP(X(6),X(110)):
523, 690

BP(X(6),X(111)):
524, 690

BP(X(6),X(825)):
824, 1491, 238p824, 752p1491, 1491p2230

BP(X(306),X(2)):
6, 647

BP(X(32),X(1492)):
824, 1491, 238p824, 752p1491, 1491p2230

BP(X(184),X(648)):
523, 686, 371p656, 372p656

BP(X(187),X(6)):
2, 523

BP(X(512),X(2)):
6, 15, 16, 6p2234

BP(X(512),X(226)):
21, 1805, 1806, 9p859


D(U,P): Cross Bicentrics Collinearity Cubics

ux(p2yz - qrx2) + vy(q2zx - rpy2) + wz(r2xy - pqz2)

D(X(1),X(3)):
3, 6, 511, 647, 523p1822, 523p1823

D(X(1),X(5)):
5, 523, 2081

D(X(2),X(55)):
6, 55, 663, 672, 650p1381, 650p1382

D(X(6),X(9)):
1, 9, 518, 650, 522p1381, 522p1382

D(X(7),X(6)):
6, 55, 663, 672, 650p1381, 650p1382

D(X(8),X(56)):
6, 56, 649, 1458, 513p1381, 513p1382

D(X(10),X(1)):
1, 6, 238, 649

D(X(11),X(109)):
6, 101, 109, 1381, 1382, 2283

D(X(19),X(6)):
3, 6, 511, 647, 523p1822, 523p1823

D(X(31),X(63)):
1, 63, 656, 1959, 525p1113, 525p1114, 684p1316

D(X(37),X(6)):
1, 6, 238, 649

D(X(42),X(2)):
1, 6, 238, 649

D(X(48),X(19)):
1, 19, 240, 4p647, 523p1113, 523p1114

D(X(55),X(57)):
1, 57, 241, 513, 514p1381, 514p1382

D(X(56),X(1)):
1, 9, 518, 650, 522p1381, 522p1382

D(X(60),X(65)):
37, 65, 661, 10p1458, 523p1381, 523p1382

D(X(63),X(25)):
6, 25, 232, 512, 661p1113, 661p1114

D(X(76),X(41)):
31, 41, 2223, 6p663, 663p1381, 663p1381

D(X(92),X(31)):
31, 48, 810, 1755, 647p1113, 647p1114

D(X(220),X(1)):
1, 57, 241, 513, 514p1381, 514p1382

D(X(255),X(1)):
1, 19, 240, 661, 523p1113, 523p1114

D(X(326),X(6)):
6, 25, 232, 512, 661p1113, 661p1114

D(X(346),X(6)):
6, 56, 649, 1458, 513p1381, 513p1382

D(X(513),X(6)):
1, 6, 43, 55, 238, 672, 1742, 6p1575

D(X(513),X(9)):
1, 9, 165, 518, 2348, 9p910, 9p1743

D(X(513),X(37)):
1, 37, 42, 846, 1045, 1757, 2238, 37p2106

D(X(514),X(1)):
1, 6, 43, 55, 238, 672, 1742, 5p1575

D(X(514),X(36)):
36, 55, 202, 203, 15p1251, 1833p2193

> D(X(514),X(37)):
6, 37, 1030, 48p424, 71p422

D(X(560),X(69)):
2, 69, 325, 525, 850p1822, 850p1823

D(X(649),X(2)):
1, 2, 9, 192, 239, 518, 1575, 2p1742

D(X(649),X(42)):
1, 37, 42, 846, 1045, 1757, 2238, 37p2106

D(X(650),X(3)):
1, 3, 1745, 1936, 3p46

D(X(650),X(55)):
1, 6, 43, 55, 238, 672, 1742, 6p1575

D(X(650),X(57)):
1, 57, 241, 910, 1279, 1419, 1743

D(X(650),X(65)):
1, 65, 73, 851, 1046, 1047, 1758, 65p416

D(X(652),X(73)):
1, 65, 73, 851, 1046, 1047, 1758, 65p416

D(X(656),X(19)):
1, 19, 204, 240, 1707, 2312, 2p1692

D(X(656),X(48)):
1, 31, 48, 1580, 1740, 1755, 1955, 31p2227

D(X(657),X(7)):
1, 7, 57, 241, 1447, 1463, 2p1423, 7p1742

D(X(661),X(2)):
2, 3, 6, 194, 385, 401, 511, 6p2227

> D(X(661),X(21)):
1, 3, 21, 416, 1936, 21p1046, 21p1047

D(X(661),X(31)):
1, 31, 48, 1580, 1740, 1755, 1955, 31p2227

D(X(661),X(63)):
1, 63, 610, 1959, 3p193, 3p230, 3p1503

D(X(661),X(81)):
1, 6, 81, 238, 1931, 2106, 58p1654, 58p1655

D(X(667),X(1)):
1, 2, 9, 192, 239, 518, 1575, 2p1742

D(X(667),X(8)):
2, 8, 144, 2p518, 2p2348, 8p910, 8p1743

D(X(667),X(10)):
2, 10, 37, 740, 1654, 1655, 2p1757, 10p2106


DP(U,P): D-Plus Cubics

ux(p2yz + qrx2) + vy(q2zx + rpy2) + wz(r2xy + pqz2)

DP(X(1),X(88)):
88, 44p1635

DP(X(1),X(100)):
100, 2087

DP(X(31),X(99)):
99, 1648

DP(X(44),X(1)):
1, 513

DP(X(75),X(99)):
99, 31p1645

DP(X(75),X(100)):
100, 31p1646

DP(X(75),X(101)):
101, 6p2087

DP(X(75),X(106)):
106, 44p1960

DP(X(75),X(110)):
110, 31p1648

DP(X(75),X(111)):
111, 31p1649

DP(X(88),X(44)):
44, 1635

DP(X(514),X(55)):
55, 15p1251, 55p506, 1833p2193

DP(X(552),X(1)):
1, 2067, 2183, 57p2066

DP(X(649),X(9)):
9, 9p506, 283p1832, 283p1833

DP(X(656),X(4)):
4, 371, 372, 4p2315

DP(X(657),X(1)):
1, 506, 15p1081, 16p554, 506p1155

DP(X(661),X(6)):
6, 15, 16, 6p2234

DP(X(663),X(2)):
2, 517, 2p2067, 7p2066

DP(X(788),X(2)):
1, 2, 239, 752, 2230

DP(X(798),X(1)):
1, 2234, 2p15, 2p16

DP(X(798),X(30)):
2, 30, 617, 298p2173, 299p2173

DP(X(810),X(92)):
1725, 2p371, 2p372, 17p473

DP(X(822),X(19)):
19, 4p15, 4p16, 19p2234

DP(X(824),X(31)):
6, 31, 1914, 6p2243, 31p2230

DP(X(1019),X(42)):
42, 10p2151, 10p2152, 42p2234

DP(X(1491),X(1)):
1, 6, 238, 2243, 6p2230

DP(X(1919),X(8)):
8, 8p506, 298p1251, 1812p1833

DP(X(1924),X(2)):
2, 298, 299, 538


Return to Front Cover