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 C2 x C18 x C18 non-normal (D4) quartic CM field invariants: 44 fields

K Quartic invariants Cl(OK) Igusa invariants Kr Reflex invariants Cl(OKr) Igusa invariants
1) [12, 2590, 1671733] C2 x C18 x C18 ---) [34117, 1295, 1323] C2 x C2 x C18 x C18
2) [17, 1838, 787373] C2 x C18 x C18 ---) [787373, 919, 14297] C18 x C36
3) [21, 1674, 659913] C2 x C18 x C18 43) [659913, 837, 10164] C2 x C18 x C18
4) [40, 1854, 244289] C2 x C18 x C18 ---) [244289, 927, 153760] C18 x C18
5) [60, 3902, 350401] C2 x C18 x C18 ---) [350401, 1951, 864000] C18 x C18
6) [77, 1038, 200061] C2 x C18 x C18 ---) [22229, 519, 17325] C6 x C18 x C18
7) [88, 1194, 356057] C2 x C18 x C18 ---) [356057, 597, 88] C2 x C2 x C18 x C252
8) [113, 5110, 5804825] C2 x C18 x C18 ---) [232193, 2555, 180800] C2 x C2 x C18 x C36
9) [129, 1776, 156444] C2 x C18 x C18 ---) [156444, 888, 158025] C2 x C18 x C36
10) [188, 3974, 3945161] C2 x C18 x C18 ---) [3945161, 1987, 752] C2 x C36 x C36
11) [248, 858, 175113] C2 x C18 x C18 36) [19457, 429, 2232] C2 x C18 x C18
12) [269, 558, 75420] C2 x C18 x C18 ---) [8380, 1116, 9684] C2 x C18 x C36
13) [485, 673, 92741] C2 x C18 x C18 ---) [92741, 1346, 81965] C18 x C18
14) [485, 1631, 18899] C2 x C18 x C18 ---) [75596, 3262, 2584565] C18 x C18
15) [629, 573, 46701] C2 x C18 x C18 ---) [5189, 1146, 141525] C18 x C18
16) [641, 214, 8885] C2 x C18 x C18 ---) [8885, 107, 641] C2 x C18 x C36
17) [748, 402, 21701] C2 x C18 x C18 ---) [21701, 201, 4675] C18 x C18
18) [872, 5142, 4600953] C2 x C18 x C18 ---) [10433, 2571, 502272] C18 x C18
19) [1037, 2510, 1371773] C2 x C18 x C18 ---) [8117, 1255, 50813] C18 x C18
20) [1129, 340, 10836] C2 x C18 x C18 ---) [301, 170, 4516] C2 x C36
21) [1129, 575, 75600] C2 x C18 x C18 ---) [21, 625, 28225] C2 x C36
22) [1129, 1182, 186705] C2 x C18 x C18 ---) [2305, 591, 40644] C4 x C288
23) [1129, 703, 21660] C2 x C18 x C18 ---) [60, 1406, 407569] C2 x C2 x C2 x C18
24) [1129, 587, 63280] C2 x C18 x C18 ---) [15820, 1174, 91449] C2 x C12 x C36
25) [1129, 195, 2450] C2 x C18 x C18 ---) [8, 390, 28225] C2 x C36
26) [1129, 531, 6984] C2 x C18 x C18 ---) [776, 1062, 254025] C4 x C36
27) [1129, 1435, 338400] C2 x C18 x C18 ---) [376, 2870, 705625] C2 x C36
28) [2444, 3928, 1508612] C2 x C18 x C18 ---) [7697, 1964, 587171] C18 x C18
29) [2712, 176, 1642] C2 x C18 x C18 ---) [6568, 352, 24408] C18 x C36
30) [6616, 748, 34020] C2 x C18 x C18 ---) [105, 374, 26464] C4 x C36
31) [6616, 730, 91875] C2 x C18 x C18 ---) [12, 410, 41350] C2 x C36
32) [10721, 873, 166410] C2 x C18 x C18 ---) [40, 1746, 96489] C2 x C2 x C36
33) [11641, 648, 207] C2 x C18 x C18 ---) [92, 1296, 419076] C2 x C2 x C18
34) [12797, 2290, 31325] C2 x C18 x C18 ---) [1253, 1145, 319925] C18 x C36
35) [19441, 835, 52800] C2 x C18 x C18 ---) [33, 1670, 486025] C2 x C36
36) [19457, 429, 2232] C2 x C18 x C18 11) [248, 858, 175113] C2 x C18 x C18
37) [20545, 599, 84564] C2 x C18 x C18 ---) [29, 513, 20545] C2 x C18
38) [43449, 491, 49408] C2 x C18 x C18 ---) [193, 982, 43449] C2 x C18
39) [61409, 915, 71136] C2 x C18 x C18 ---) [1976, 1830, 552681] C2 x C2 x C18 x C18
40) [65164, 1534, 1813] C2 x C18 x C18 ---) [37, 767, 146619] C18 x C18
41) [128569, 359, 78] C2 x C18 x C18 ---) [312, 718, 128569] C2 x C18 x C36
42) [270349, 607, 24525] C2 x C18 x C18 ---) [109, 1214, 270349] C18 x C18
43) [659913, 837, 10164] C2 x C18 x C18 3) [21, 1674, 659913] C2 x C18 x C18
44) [13756969, 3763, 100800] C2 x C18 x C18 ---) [28, 7526, 13756969] C18 x C18