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 C72 non-normal (D4) quartic CM field invariants: 56 fields

K Quartic invariants Cl(OK) Igusa invariants Kr Reflex invariants Cl(OKr) Igusa invariants
1) [316, 1214, 357073] C3 x C3 x C72 ---) [357073, 607, 2844] C3 x C72
2) [316, 504, 25268] C3 x C3 x C72 ---) [6317, 252, 9559] C3 x C72
3) [321, 458, 51157] C3 x C3 x C72 ---) [51157, 229, 321] C3 x C72
4) [321, 1662, 438897] C3 x C3 x C72 ---) [438897, 831, 62916] C6 x C36
5) [344, 2134, 1088953] C3 x C3 x C72 50) [1088953, 1067, 12384] C3 x C3 x C72
6) [413, 379, 30851] C3 x C3 x C72 ---) [123404, 758, 20237] C3 x C3 x C6 x C36
7) [568, 306, 9209] C3 x C3 x C72 ---) [9209, 153, 3550] C3 x C72
8) [824, 542, 13907] C3 x C3 x C72 ---) [55628, 1084, 238136] C3 x C6 x C36
9) [892, 1842, 526229] C3 x C3 x C72 ---) [4349, 921, 80503] C3 x C72
10) [1937, 1195, 3988] C3 x C3 x C72 ---) [997, 865, 156897] C3 x C36
11) [2177, 1391, 195812] C3 x C3 x C72 30) [48953, 2782, 1151633] C3 x C3 x C72
12) [8828, 2038, 473369] C3 x C3 x C72 ---) [2801, 1019, 141248] C3 x C72
13) [9833, 204, 571] C3 x C3 x C72 ---) [2284, 408, 39332] C3 x C72
14) [11757, 218, 124] C3 x C3 x C72 ---) [124, 436, 47028] C6 x C36
15) [12409, 2245, 363456] C3 x C3 x C72 ---) [2524, 4490, 3586201] C3 x C24
16) [15733, 330, 11492] C3 x C3 x C72 ---) [17, 660, 62932] C6 x C36
17) [15881, 586, 22325] C3 x C3 x C72 ---) [893, 293, 15881] C3 x C72
18) [17609, 139, 428] C3 x C3 x C72 ---) [428, 278, 17609] C3 x C72
19) [17929, 477, 52400] C3 x C3 x C72 ---) [524, 954, 17929] C3 x C72
20) [24533, 362, 8228] C3 x C3 x C72 ---) [17, 724, 98132] C6 x C36
21) [27289, 667, 104400] C3 x C3 x C72 ---) [29, 609, 27289] C3 x C18
22) [27833, 430, 18392] C3 x C3 x C72 ---) [152, 860, 111332] C3 x C18
23) [30677, 887, 4961] C3 x C3 x C72 ---) [41, 709, 122708] C6 x C36
24) [38593, 2122, 971349] C3 x C3 x C72 ---) [141, 1061, 38593] C3 x C72
25) [40472, 410, 1553] C3 x C3 x C72 ---) [1553, 205, 10118] C3 x C72
26) [42817, 227, 2178] C3 x C3 x C72 ---) [8, 454, 42817] C2 x C36
27) [45244, 448, 4932] C3 x C3 x C72 ---) [137, 224, 11311] C3 x C72
28) [46193, 1575, 54292] C3 x C3 x C72 ---) [277, 3150, 2263457] C3 x C72
29) [48028, 8338, 12577761] C3 x C3 x C72 ---) [3169, 4169, 1200700] C3 x C72
30) [48953, 2782, 1151633] C3 x C3 x C72 11) [2177, 1391, 195812] C3 x C3 x C72
31) [51509, 962, 25325] C3 x C3 x C72 ---) [1013, 481, 51509] C3 x C72
32) [73148, 716, 55016] C3 x C3 x C72 ---) [104, 358, 18287] C6 x C72
33) [75644, 756, 67240] C3 x C3 x C72 ---) [40, 378, 18911] C6 x C72
34) [93241, 467, 31212] C3 x C3 x C72 ---) [12, 934, 93241] C3 x C72
35) [111597, 1005, 1413] C3 x C3 x C72 ---) [157, 2010, 1004373] C3 x C72
36) [126949, 1426, 573] C3 x C3 x C72 ---) [573, 713, 126949] C3 x C72
37) [133761, 2459, 675664] C3 x C3 x C72 ---) [349, 4918, 3344025] C3 x C72
38) [147484, 4232, 3150100] C3 x C3 x C72 ---) [109, 2116, 331839] C3 x C72
39) [182636, 1710, 481] C3 x C3 x C72 ---) [481, 855, 182636] C6 x C72
40) [186364, 3534, 2376833] C3 x C3 x C72 ---) [233, 1767, 186364] C3 x C72
41) [226897, 3391, 95232] C3 x C3 x C72 ---) [93, 3165, 2042073] C6 x C36
42) [238233, 539, 13072] C3 x C3 x C72 ---) [817, 1078, 238233] C6 x C180
43) [250748, 514, 3362] C3 x C3 x C72 ---) [8, 514, 62687] C72
44) [296845, 545, 45] C3 x C3 x C72 ---) [5, 1090, 296845] C3 x C18
45) [385889, 719, 32768] C3 x C3 x C72 ---) [8, 1438, 385889] C3 x C72
46) [693457, 887, 23328] C3 x C3 x C72 ---) [8, 1774, 693457] C3 x C72
47) [711517, 907, 27783] C3 x C3 x C72 ---) [28, 1814, 711517] C3 x C72
48) [883417, 997, 27648] C3 x C3 x C72 ---) [12, 1994, 883417] C6 x C36
49) [922273, 967, 3204] C3 x C3 x C72 ---) [89, 1934, 922273] C3 x C72
50) [1088953, 1067, 12384] C3 x C3 x C72 5) [344, 2134, 1088953] C3 x C3 x C72
51) [1183673, 1109, 11552] C3 x C3 x C72 ---) [8, 2218, 1183673] C6 x C36
52) [1540969, 1363, 79200] C3 x C3 x C72 ---) [88, 2726, 1540969] C3 x C72
53) [2442201, 1787, 187792] C3 x C3 x C72 ---) [97, 3574, 2442201] C3 x C72
54) [5142601, 2293, 28812] C3 x C3 x C72 ---) [12, 4586, 5142601] C6 x C36
55) [7823161, 2797, 12] C3 x C3 x C72 ---) [12, 5594, 7823161] C3 x C72
56) [8830057, 2995, 34992] C3 x C3 x C72 ---) [12, 5990, 8830057] C6 x C36