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 C6 x C54 non-normal (D4) quartic CM field invariants: 50 fields

K Quartic invariants Cl(OK) Igusa invariants Kr Reflex invariants Cl(OKr) Igusa invariants
1) [12, 3658, 3302041] C3 x C6 x C54 ---) [3302041, 1829, 10800] C3 x C3 x C108
2) [229, 510, 50369] C3 x C6 x C54 ---) [50369, 255, 3664] C6 x C6 x C54
3) [257, 426, 44341] C3 x C6 x C54 ---) [44341, 213, 257] C2 x C6 x C54
4) [469, 2550, 1355481] C3 x C6 x C54 ---) [150609, 1275, 67536] C6 x C108
5) [469, 299, 12853] C3 x C6 x C54 ---) [12853, 598, 37989] C6 x C54
6) [469, 762, 53237] C3 x C6 x C54 ---) [53237, 381, 22981] C3 x C108
7) [469, 970, 233349] C3 x C6 x C54 ---) [233349, 485, 469] C3 x C108
8) [1229, 1399, 68675] C3 x C6 x C54 ---) [10988, 2798, 1682501] C2 x C6 x C54
9) [1901, 605, 34001] C3 x C6 x C54 ---) [281, 1210, 230021] C3 x C108
10) [1901, 858, 62377] C3 x C6 x C54 ---) [1273, 429, 30416] C6 x C54
11) [2557, 1552, 591948] C3 x C6 x C54 ---) [812, 776, 2557] C6 x C108
12) [2981, 690, 11709] C3 x C6 x C54 ---) [1301, 345, 26829] C6 x C54
13) [3593, 949, 181136] C3 x C6 x C54 ---) [11321, 1898, 176057] C3 x C3 x C6 x C270
14) [7244, 1038, 8577] C3 x C6 x C54 ---) [953, 519, 65196] C6 x C54
15) [7481, 2054, 306629] C3 x C6 x C54 ---) [1061, 1027, 187025] C3 x C108
16) [7673, 1541, 39296] C3 x C6 x C54 ---) [2456, 3082, 2217497] C6 x C54
17) [7948, 1252, 2424] C3 x C6 x C54 ---) [2424, 626, 97363] C6 x C108
18) [10636, 690, 23301] C3 x C6 x C54 ---) [2589, 345, 23931] C3 x C3 x C108
19) [14296, 490, 2841] C3 x C6 x C54 ---) [2841, 245, 14296] C6 x C54
20) [15641, 2114, 866993] C3 x C6 x C54 ---) [233, 1057, 62564] C6 x C54
21) [16369, 2058, 11225] C3 x C6 x C54 ---) [449, 1029, 261904] C6 x C54
22) [16689, 131, 118] C3 x C6 x C54 ---) [472, 262, 16689] C6 x C54
23) [21737, 155, 572] C3 x C6 x C54 ---) [572, 310, 21737] C2 x C6 x C54
24) [23417, 539, 19942] C3 x C6 x C54 ---) [472, 1078, 210753] C6 x C54
25) [28097, 1021, 197392] C3 x C6 x C54 ---) [73, 1341, 449552] C6 x C54
26) [28669, 671, 105393] C3 x C6 x C54 ---) [57, 1249, 114676] C6 x C54
27) [31532, 5374, 4066769] C3 x C6 x C54 ---) [1841, 2687, 788300] C3 x C108
28) [32009, 387, 29440] C3 x C6 x C54 ---) [460, 774, 32009] C2 x C108
29) [55768, 250, 1683] C3 x C6 x C54 ---) [748, 500, 55768] C2 x C6 x C54
30) [69196, 530, 1029] C3 x C6 x C54 ---) [21, 265, 17299] C3 x C108
31) [69196, 3224, 868644] C3 x C6 x C54 ---) [2681, 1612, 432475] C3 x C108
32) [69196, 622, 27525] C3 x C6 x C54 ---) [1101, 311, 17299] C3 x C3 x C108
33) [105709, 1306, 3573] C3 x C6 x C54 ---) [397, 653, 105709] C3 x C54
34) [119321, 1400, 12716] C3 x C6 x C54 ---) [44, 700, 119321] C6 x C54
35) [152333, 1315, 89557] C3 x C6 x C54 ---) [13, 783, 152333] C6 x C54
36) [159449, 507, 24400] C3 x C6 x C54 ---) [61, 1014, 159449] C3 x C54
37) [175429, 421, 453] C3 x C6 x C54 ---) [453, 842, 175429] C3 x C108
38) [178033, 4784, 1270839] C3 x C6 x C54 ---) [444, 9568, 17803300] C6 x C108
39) [192616, 1766, 9225] C3 x C6 x C54 ---) [41, 883, 192616] C3 x C54
40) [195549, 503, 14365] C3 x C6 x C54 ---) [85, 1006, 195549] C6 x C108
41) [200589, 449, 253] C3 x C6 x C54 ---) [253, 898, 200589] C3 x C108
42) [295041, 1092, 3075] C3 x C6 x C54 ---) [492, 2184, 1180164] C6 x C108
43) [306217, 1703, 36064] C3 x C6 x C54 ---) [184, 3406, 2755953] C3 x C108
44) [515932, 2878, 6993] C3 x C6 x C54 ---) [777, 1439, 515932] C6 x C216
45) [535393, 2285, 100672] C3 x C6 x C54 ---) [13, 1523, 535393] C6 x C54
46) [599009, 3905, 68450] C3 x C6 x C54 ---) [8, 7810, 14975225] C3 x C108
47) [1220561, 3387, 121680] C3 x C6 x C54 ---) [5, 6774, 10985049] C6 x C54
48) [1692485, 1301, 29] C3 x C6 x C54 ---) [29, 2602, 1692485] C3 x C54
49) [1712049, 3947, 42592] C3 x C6 x C54 ---) [88, 7894, 15408441] C3 x C108
50) [3842089, 3283, 1734000] C3 x C6 x C54 ---) [60, 6566, 3842089] C6 x C108