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 C9 x C72 non-normal (D4) quartic CM field invariants: 58 fields

K Quartic invariants Cl(OK) Igusa invariants Kr Reflex invariants Cl(OKr) Igusa invariants
1) [5, 10033, 25163741] C9 x C72 58) [25163741, 7481, 7700405] C9 x C72
2) [28, 2454, 1166729] C9 x C72 55) [1166729, 1227, 84700] C9 x C72
3) [28, 3590, 3221017] C9 x C72 ---) [3221017, 1795, 252] C3 x C9 x C72
4) [76, 5958, 8727305] C9 x C72 ---) [8727305, 2979, 36784] C36 x C36
5) [104, 1668, 475492] C9 x C72 ---) [118873, 834, 55016] C9 x C36
6) [137, 7702, 11664953] C9 x C72 ---) [11664953, 3851, 791312] C9 x C720
7) [177, 2138, 1136389] C9 x C72 ---) [1136389, 1069, 1593] C9 x C9 x C72
8) [376, 1086, 30803] C9 x C72 ---) [123212, 2172, 1056184] C3 x C18 x C36
9) [508, 1014, 110237] C9 x C72 ---) [110237, 507, 36703] C9 x C360
10) [541, 2366, 698353] C9 x C72 ---) [698353, 1183, 175284] C36 x C72
11) [653, 2258, 10433] C9 x C72 ---) [10433, 1129, 316052] C18 x C36
12) [908, 1160, 226532] C9 x C72 44) [56633, 580, 27467] C9 x C72
13) [1061, 2663, 200225] C9 x C72 ---) [8009, 1633, 424400] C18 x C36
14) [1129, 231, 6284] C9 x C72 ---) [6284, 462, 28225] C72
15) [1129, 1335, 438500] C9 x C72 ---) [4385, 1867, 72256] C144
16) [1129, 1021, 84204] C9 x C72 ---) [9356, 2042, 705625] C72
17) [1129, 445, 35676] C9 x C72 ---) [3964, 890, 55321] C72
18) [1129, 469, 47934] C9 x C72 ---) [21304, 938, 28225] C72
19) [1129, 375, 1004] C9 x C72 ---) [1004, 750, 136609] C72
20) [1244, 7198, 7857377] C9 x C72 45) [64937, 3599, 1273856] C9 x C72
21) [1669, 1268, 320175] C9 x C72 28) [5692, 2536, 327124] C9 x C72
22) [1757, 521, 46337] C9 x C72 ---) [46337, 1042, 86093] C9 x C360
23) [1797, 1322, 429733] C9 x C72 53) [429733, 661, 1797] C9 x C72
24) [2733, 2491, 402727] C9 x C72 ---) [9532, 4982, 4594173] C18 x C36
25) [3137, 103, 1868] C9 x C72 ---) [1868, 206, 3137] C72
26) [4409, 611, 4048] C9 x C72 ---) [253, 933, 216041] C72
27) [5521, 511, 63900] C9 x C72 ---) [284, 1022, 5521] C72
28) [5692, 2536, 327124] C9 x C72 21) [1669, 1268, 320175] C9 x C72
29) [6616, 1654, 22329] C9 x C72 ---) [2481, 827, 165400] C2 x C36
30) [7573, 109, 1077] C9 x C72 ---) [1077, 218, 7573] C72
31) [7573, 313, 22599] C9 x C72 ---) [124, 626, 7573] C72
32) [10721, 594, 45325] C9 x C72 ---) [37, 297, 10721] C72
33) [13069, 232, 387] C9 x C72 ---) [172, 464, 52276] C2 x C36
34) [14876, 124, 125] C9 x C72 ---) [5, 248, 14876] C72
35) [14876, 614, 1274] C9 x C72 ---) [104, 574, 3719] C2 x C72
36) [14876, 132, 637] C9 x C72 ---) [13, 264, 14876] C72
37) [17273, 1075, 77312] C9 x C72 ---) [1208, 2150, 846377] C2 x C36
38) [24581, 316, 383] C9 x C72 ---) [1532, 632, 98324] C18 x C36
39) [31897, 551, 4132] C9 x C72 ---) [1033, 1102, 287073] C72
40) [42421, 337, 17787] C9 x C72 ---) [12, 674, 42421] C2 x C36
41) [43256, 532, 27500] C9 x C72 ---) [44, 266, 10814] C2 x C36
42) [43256, 208, 2] C9 x C72 ---) [8, 208, 10814] C72
43) [52753, 439, 34992] C9 x C72 ---) [12, 878, 52753] C2 x C36
44) [56633, 580, 27467] C9 x C72 12) [908, 1160, 226532] C9 x C72
45) [64937, 3599, 1273856] C9 x C72 20) [1244, 7198, 7857377] C9 x C72
46) [82673, 299, 1682] C9 x C72 ---) [8, 598, 82673] C2 x C36
47) [90268, 338, 5994] C9 x C72 ---) [296, 676, 90268] C18 x C72
48) [117289, 1410, 27869] C9 x C72 ---) [29, 705, 117289] C9 x C18
49) [132369, 719, 96148] C9 x C72 ---) [13, 1201, 132369] C72
50) [143036, 758, 605] C9 x C72 ---) [5, 379, 35759] C72
51) [212753, 571, 28322] C9 x C72 ---) [8, 1142, 212753] C2 x C36
52) [368833, 613, 1734] C9 x C72 ---) [24, 1226, 368833] C72
53) [429733, 661, 1797] C9 x C72 23) [1797, 1322, 429733] C9 x C72
54) [514561, 2243, 100000] C9 x C72 ---) [40, 4486, 4631049] C144
55) [1166729, 1227, 84700] C9 x C72 2) [28, 2454, 1166729] C9 x C72
56) [1953989, 2197, 718205] C9 x C72 ---) [5, 2801, 1953989] C72
57) [13797161, 4019, 588800] C9 x C72 ---) [92, 8038, 13797161] C18 x C36
58) [25163741, 7481, 7700405] C9 x C72 1) [5, 10033, 25163741] C9 x C72