Genus 2 Curves Database Igusa CM Invariants Database Quartic CM Fields Database

A quartic CM field field K is represented by invariants [D,A,B], where K = Q[x]/(x4+Ax2+B), and D is the discriminant of the totally real quadratic subfield (hence A2-4B = m2D for some m).

Class number: [Non-normal] [Cyclic]

[1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23] [24]
[25] [26] [27] [28] [29] [30] [31] [32] [33] [34] [35] [36] [37] [38] [39] [40] [41] [42] [43] [44] [45] [46] [47] [48]
[49] [50] [51] [52] [53] [54] [55] [56] [57] [58] [59] [60] [61] [62] [63] [64] [65] [66] [67] [68] [69] [70] [71] [72]
[73] [74] [75] [76] [77] [78] [79] [80] [81] [82] [83] [84] [85] [86] [87] [88] [89] [90] [91] [92] [93] [94] [95] [96]
[97] [98] [99] [100] [101] [102] [103] [104] [105] [106] [107] [108] [109] [110] [111] [112] [113] [114] [115] [116] [117] [118] [119] [120]
[121] [122] [123] [124] [125] [126] [127] [128] [129] [130] [131] [132] [133] [134] [135] [136] [137] [138] [139] [140] [141] [142] [143] [144]
[145] [146] [147] [148] [149] [150] [151] [152] [153] [154] [155] [156] [157] [158] [159] [160] [161] [162] [163] [164] [165] [166] [167] [168]
[169] [170] [171] [172] [173] [174] [175] [176] [177] [178] [179] [180] [181] [182] [183] [184] [185] [186] [187] [188] [189] [190] [191] [192]
[193] [194] [195] [196] [197] [198] [199] [200] [201] [202] [203] [204] [205] [206] [207] [208] [209] [210] [211] [212] [213] [214] [215] [216]
[217] [218] [219] [220] [221] [222] [223] [224] [225] [226] [227] [228] [229] [230] [231] [232] [233] [234] [235] [236] [237] [238] [239] [240]
[241] [242] [243] [244] [245] [246] [247] [248] [249] [250] [251] [252] [253] [254] [255] [256] [257] [258] [259] [260] [261] [262] [263] [264]
[265] [266] [267] [268] [269] [270] [271] [272] [273] [274] [275] [276] [277] [278] [279] [280] [281] [282] [283] [284] [285] [286] [287] [288]
[289] [290] [291] [292] [293] [294] [295] [296] [297] [298] [299] [300] [301] [302] [303] [304] [305] [306] [307] [308] [309] [310] [311] [312]
[313] [314] [315] [316] [317] [318] [319] [320] [321] [322] [323] [324] [325] [326] [327] [328] [329] [330] [331] [332] [333] [334] [335] [336]
[337] [338] [339] [340] [341] [342] [343] [344] [345] [346] [347] [348] [349] [350] [351] [352] [353] [354] [355] [356] [357] [358] [359] [360]
[361] [362] [363] [364] [365] [366] [367] [368] [369] [370] [371] [372] [373] [374] [375] [376] [377] [378] [379] [380] [381] [382] [383] [384]
[385] [386] [387] [388] [389] [390] [391] [392] [393] [394] [395] [396] [397] [398] [399] [400] [401] [402] [403] [404] [405] [406] [407] [408]
[409] [410] [411] [412] [413] [414] [415] [416] [417] [418] [419] [420] [421] [422] [423] [424] [425] [426] [427] [428] [429] [430] [431] [432]
[433] [434] [435] [436] [437] [438] [439] [440] [441] [442] [443] [444] [445] [446] [447] [448] [449] [450] [451] [452] [453] [454] [455] [456]
[457] [458] [459] [460] [461] [462] [463] [464] [465] [466] [467] [468] [469] [470] [471] [472] [473] [474] [475] [476] [477] [478] [479] [480]
[481] [482] [483] [484] [485] [486] [487] [488] [489] [490] [491] [492] [493] [494] [495] [496] [497] [498] [499] [500] [501] [502] [503] [504]
[505] [506] [507] [508] [509] [510] [511] [512] [513] [514] [515] [516] [517] [518] [519] [520] [521] [522] [523] [524] [525] [526] [527] [528]
[529] [530] [531] [532] [533] [534] [535] [536] [537] [538] [539] [540] [541] [542] [543] [544] [545] [546] [547] [548] [549] [550] [551] [552]
[553] [554] [555] [556] [557] [558] [559] [560] [561] [562] [563] [564] [565] [566] [567] [568] [569] [570] [571] [572] [573] [574] [575] [576]

Class group C3 x C3 x C36 non-normal (D4) quartic CM field invariants: 48 fields

K Quartic invariants Cl(OK) Igusa invariants Kr Reflex invariants Cl(OKr) Igusa invariants
1) [229, 3686, 99049] C3 x C3 x C36 ---) [99049, 1843, 824400] C3 x C360
2) [469, 642, 11117] C3 x C3 x C36 ---) [11117, 321, 22981] C3 x C36
3) [469, 155, 4951] C3 x C3 x C36 ---) [19804, 310, 4221] C6 x C18
4) [469, 1522, 487197] C3 x C3 x C36 ---) [54133, 761, 22981] C3 x C36
5) [892, 296, 13876] C3 x C3 x C36 ---) [3469, 148, 2007] C3 x C36
6) [1229, 193, 9005] C3 x C3 x C36 ---) [9005, 386, 1229] C6 x C36
7) [1257, 719, 76132] C3 x C3 x C36 ---) [19033, 1438, 212433] C6 x C18
8) [2089, 1469, 100278] C3 x C3 x C36 ---) [4952, 2938, 1756849] C3 x C36
9) [2589, 2201, 226633] C3 x C3 x C36 ---) [1873, 1383, 372816] C3 x C36
10) [2777, 377, 18176] C3 x C3 x C36 ---) [284, 754, 69425] C3 x C36
11) [3356, 234, 265] C3 x C3 x C36 ---) [265, 117, 3356] C6 x C36
12) [3877, 437, 249] C3 x C3 x C36 ---) [249, 874, 189973] C3 x C36
13) [3957, 195, 603] C3 x C3 x C36 ---) [268, 390, 35613] C6 x C18
14) [5497, 99, 1076] C3 x C3 x C36 ---) [269, 198, 5497] C3 x C36
15) [7537, 743, 45684] C3 x C3 x C36 ---) [141, 973, 188425] C3 x C36
16) [7721, 530, 736] C3 x C3 x C36 ---) [184, 1060, 277956] C6 x C18
17) [9281, 183, 6052] C3 x C3 x C36 ---) [1513, 366, 9281] C6 x C36
18) [10273, 214, 1176] C3 x C3 x C36 ---) [24, 428, 41092] C3 x C12
19) [15593, 851, 177152] C3 x C3 x C36 ---) [173, 1585, 15593] C3 x C36
20) [27065, 171, 544] C3 x C3 x C36 ---) [136, 342, 27065] C3 x C36
21) [32009, 1259, 4160] C3 x C3 x C36 ---) [65, 887, 128036] C72
22) [34492, 2318, 101569] C3 x C3 x C36 ---) [601, 1159, 310428] C3 x C36
23) [36553, 591, 5076] C3 x C3 x C36 ---) [141, 1182, 328977] C6 x C18
24) [40069, 802, 525] C3 x C3 x C36 ---) [21, 401, 40069] C3 x C6
25) [44033, 1170, 166093] C3 x C3 x C36 ---) [37, 585, 44033] C3 x C36
26) [49897, 1119, 200772] C3 x C3 x C36 ---) [33, 895, 199588] C3 x C18
27) [55973, 253, 2009] C3 x C3 x C36 ---) [41, 506, 55973] C3 x C36
28) [59061, 1181, 333925] C3 x C3 x C36 ---) [37, 1461, 531549] C3 x C12
29) [84093, 291, 147] C3 x C3 x C36 ---) [12, 582, 84093] C6 x C18
30) [94345, 734, 40344] C3 x C3 x C36 ---) [24, 1468, 377380] C3 x C18
31) [94397, 3297, 806013] C3 x C3 x C36 ---) [13, 1845, 849573] C6 x C18
32) [120937, 1759, 17664] C3 x C3 x C36 ---) [69, 3009, 1088433] C3 x C36
33) [127393, 728, 5103] C3 x C3 x C36 ---) [28, 1456, 509572] C6 x C18
34) [141601, 403, 5202] C3 x C3 x C36 ---) [8, 806, 141601] C3 x C36
35) [155321, 747, 100672] C3 x C3 x C36 ---) [13, 1353, 155321] C3 x C36
36) [169649, 457, 9800] C3 x C3 x C36 ---) [8, 914, 169649] C3 x C36
37) [188329, 677, 67500] C3 x C3 x C36 ---) [12, 1354, 188329] C6 x C18
38) [221341, 1637, 171925] C3 x C3 x C36 ---) [13, 941, 221341] C3 x C18
39) [228457, 505, 6642] C3 x C3 x C36 ---) [328, 1010, 228457] C12 x C36
40) [255928, 994, 183027] C3 x C3 x C36 ---) [12, 506, 63982] C6 x C18
41) [284593, 967, 162624] C3 x C3 x C36 ---) [21, 1934, 284593] C3 x C36
42) [325177, 571, 216] C3 x C3 x C36 ---) [24, 1142, 325177] C3 x C18
43) [410393, 667, 8624] C3 x C3 x C36 ---) [44, 1334, 410393] C3 x C36
44) [682781, 841, 6125] C3 x C3 x C36 ---) [5, 1682, 682781] C3 x C36
45) [781969, 2794, 1169640] C3 x C3 x C36 ---) [40, 5588, 3127876] C3 x C72
46) [1434217, 1267, 42768] C3 x C3 x C36 ---) [33, 2534, 1434217] C3 x C36
47) [1771129, 2509, 1130988] C3 x C3 x C36 ---) [12, 5018, 1771129] C6 x C18
48) [2124713, 2675, 1257728] C3 x C3 x C36 ---) [17, 5350, 2124713] C3 x C36