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 C5 x C55 non-normal (D4) quartic CM field invariants: 47 fields

K Quartic invariants Cl(OK) Igusa invariants Kr Reflex invariants Cl(OKr) Igusa invariants
1) [5, 2878, 2038721] C5 x C55 46) [2038721, 1439, 8000] C5 x C55
2) [5, 6134, 9155609] C5 x C55 47) [9155609, 3067, 62720] C5 x C55
3) [5, 6494, 9191009] C5 x C55 ---) [9191009, 3247, 338000] C5 x C715
4) [5, 5686, 8077529] C5 x C55 ---) [8077529, 2843, 1280] C5 x C165
5) [13, 1777, 788701] C5 x C55 43) [788701, 3061, 567853] C5 x C55
6) [13, 2430, 1313153] C5 x C55 45) [1313153, 1215, 40768] C5 x C55
7) [29, 1437, 463861] C5 x C55 40) [463861, 2874, 209525] C5 x C55
8) [149, 994, 198733] C5 x C55 35) [198733, 497, 12069] C5 x C55
9) [181, 1361, 379413] C5 x C55 ---) [42157, 2722, 334669] C5 x C5 x C55
10) [233, 2422, 1227929] C5 x C55 ---) [1227929, 1211, 59648] C5 x C165
11) [401, 1774, 10433] C5 x C55 ---) [10433, 887, 194084] C55
12) [401, 2918, 2026025] C5 x C55 31) [81041, 1459, 25664] C5 x C55
13) [401, 2783, 1907300] C5 x C55 ---) [19073, 2327, 1348964] C55
14) [1093, 369, 977] C5 x C55 ---) [977, 738, 132253] C55
15) [1093, 1202, 7069] C5 x C55 ---) [7069, 601, 88533] C55
16) [2153, 891, 172096] C5 x C55 ---) [2689, 1782, 105497] C55
17) [3833, 2215, 880628] C5 x C55 ---) [4493, 4430, 1383713] C5 x C165
18) [4357, 2378, 2053] C5 x C55 ---) [2053, 1189, 352917] C55
19) [5189, 346, 9173] C5 x C55 20) [9173, 173, 5189] C5 x C55
20) [9173, 173, 5189] C5 x C55 19) [5189, 346, 9173] C5 x C55
21) [10909, 341, 4525] C5 x C55 ---) [181, 682, 98181] C55
22) [14281, 1287, 324836] C5 x C55 ---) [281, 2003, 228496] C55
23) [15473, 538, 10469] C5 x C55 ---) [29, 269, 15473] C55
24) [18253, 1537, 366993] C5 x C55 ---) [337, 2035, 657108] C55
25) [18353, 3014, 1096457] C5 x C55 ---) [593, 1507, 293648] C55
26) [18353, 735, 130468] C5 x C55 ---) [193, 1470, 18353] C55
27) [37253, 994, 97997] C5 x C55 ---) [53, 497, 37253] C55
28) [44741, 629, 87725] C5 x C55 ---) [29, 1033, 44741] C55
29) [50969, 787, 142100] C5 x C55 ---) [29, 949, 50969] C55
30) [63761, 271, 2420] C5 x C55 ---) [5, 542, 63761] C55
31) [81041, 1459, 25664] C5 x C55 12) [401, 2918, 2026025] C5 x C55
32) [109253, 1221, 345397] C5 x C55 ---) [13, 717, 109253] C55
33) [110237, 345, 2197] C5 x C55 ---) [13, 690, 110237] C55
34) [141937, 607, 56628] C5 x C55 ---) [13, 1214, 141937] C55
35) [198733, 497, 12069] C5 x C55 8) [149, 994, 198733] C5 x C55
36) [249449, 787, 92480] C5 x C55 ---) [5, 1001, 249449] C55
37) [287849, 1043, 200000] C5 x C55 ---) [5, 1129, 287849] C55
38) [291457, 1567, 541008] C5 x C55 ---) [13, 1325, 291457] C55
39) [314329, 561, 98] C5 x C55 ---) [8, 1122, 314329] C55
40) [463861, 2874, 209525] C5 x C55 7) [29, 1437, 463861] C5 x C55
41) [589481, 947, 76832] C5 x C55 ---) [8, 1894, 589481] C55
42) [690629, 853, 9245] C5 x C55 ---) [5, 1706, 690629] C55
43) [788701, 3061, 567853] C5 x C55 5) [13, 1777, 788701] C5 x C55
44) [813017, 977, 35378] C5 x C55 ---) [8, 1954, 813017] C55
45) [1313153, 1215, 40768] C5 x C55 6) [13, 2430, 1313153] C5 x C55
46) [2038721, 1439, 8000] C5 x C55 1) [5, 2878, 2038721] C5 x C55
47) [9155609, 3067, 62720] C5 x C55 2) [5, 6134, 9155609] C5 x C55