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 C45 non-normal (D4) quartic CM field invariants: 21 fields

K Quartic invariants Cl(OK) Igusa invariants Kr Reflex invariants Cl(OKr) Igusa invariants
1) [229, 546, 73613] C3 x C3 x C45 ---) [73613, 273, 229] C3 x C45
2) [761, 562, 2861] C3 x C3 x C45 ---) [2861, 281, 19025] C3 x C45
3) [1129, 1635, 44816] C3 x C3 x C45 ---) [2801, 1231, 221284] C3 x C15
4) [1373, 1838, 295361] C3 x C3 x C45 ---) [2441, 919, 137300] C3 x C45
5) [1901, 1994, 621413] C3 x C3 x C45 ---) [3677, 997, 93149] C3 x C45
6) [1901, 1321, 412973] C3 x C3 x C45 ---) [3413, 2642, 93149] C3 x C45
7) [3137, 611, 86272] C3 x C3 x C45 ---) [337, 927, 12548] C3 x C15
8) [3221, 1094, 247673] C3 x C3 x C45 ---) [857, 547, 12884] C3 x C45
9) [7481, 5574, 106825] C3 x C3 x C45 ---) [4273, 2787, 1915136] C3 x C45
10) [10069, 2026, 19269] C3 x C3 x C45 ---) [2141, 1013, 251725] C3 x C45
11) [15773, 2282, 734053] C3 x C3 x C45 ---) [397, 1141, 141957] C3 x C45
12) [16673, 1699, 17216] C3 x C3 x C45 ---) [269, 1321, 416825] C3 x C45
13) [18661, 8525, 11073061] C3 x C3 x C45 ---) [3181, 4721, 5393029] C15 x C45
14) [23993, 866, 91517] C3 x C3 x C45 ---) [173, 433, 23993] C3 x C45
15) [32009, 259, 8768] C3 x C3 x C45 ---) [137, 518, 32009] C45
16) [35597, 1321, 197] C3 x C3 x C45 ---) [197, 2642, 1744253] C3 x C45
17) [114889, 339, 8] C3 x C3 x C45 ---) [8, 678, 114889] C45
18) [131797, 485, 25857] C3 x C3 x C45 ---) [17, 970, 131797] C3 x C45
19) [1043657, 1411, 236816] C3 x C3 x C45 ---) [41, 2822, 1043657] C3 x C45
20) [1576781, 1649, 285605] C3 x C3 x C45 ---) [5, 2557, 1576781] C3 x C45
21) [3283433, 2131, 314432] C3 x C3 x C45 ---) [17, 4262, 3283433] C3 x C45