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 C65 non-normal (D4) quartic CM field invariants: 53 fields

K Quartic invariants Cl(OK) Igusa invariants Kr Reflex invariants Cl(OKr) Igusa invariants
1) [5, 2757, 1882561] C5 x C65 53) [1882561, 1919, 450000] C5 x C65
2) [13, 1873, 876301] C5 x C65 52) [876301, 3229, 634933] C5 x C65
3) [89, 1186, 351293] C5 x C65 48) [351293, 593, 89] C5 x C65
4) [293, 1018, 164149] C5 x C65 44) [164149, 509, 23733] C5 x C65
5) [293, 1037, 157429] C5 x C65 ---) [157429, 2074, 445653] C65 x C65
6) [401, 983, 89092] C5 x C65 ---) [22273, 1966, 609921] C65
7) [797, 610, 64333] C5 x C65 40) [64333, 305, 7173] C5 x C65
8) [1093, 161, 4021] C5 x C65 ---) [4021, 322, 9837] C65
9) [1093, 1178, 307573] C5 x C65 ---) [6277, 589, 9837] C65
10) [1093, 877, 21501] C5 x C65 ---) [2389, 1489, 482013] C65
11) [1429, 645, 761] C5 x C65 ---) [761, 987, 142900] C195
12) [1429, 3786, 10949] C5 x C65 ---) [10949, 1893, 893125] C195
13) [2081, 742, 4457] C5 x C65 ---) [4457, 371, 33296] C65
14) [2281, 1719, 642368] C5 x C65 26) [10037, 3438, 385489] C5 x C65
15) [2309, 233, 8377] C5 x C65 24) [8377, 466, 20781] C5 x C65
16) [2381, 2121, 952633] C5 x C65 ---) [7873, 4242, 688109] C5 x C585
17) [3089, 2223, 493300] C5 x C65 ---) [4933, 3701, 3363921] C5 x C195
18) [4157, 269, 8737] C5 x C65 25) [8737, 538, 37413] C5 x C65
19) [4441, 371, 33300] C5 x C65 ---) [37, 401, 39969] C65
20) [6481, 491, 19764] C5 x C65 ---) [61, 521, 58329] C65
21) [7229, 581, 68125] C5 x C65 ---) [109, 861, 180725] C65
22) [7229, 1405, 188081] C5 x C65 ---) [521, 1835, 28916] C65
23) [7817, 354, 61] C5 x C65 ---) [61, 177, 7817] C65
24) [8377, 466, 20781] C5 x C65 15) [2309, 233, 8377] C5 x C65
25) [8737, 538, 37413] C5 x C65 18) [4157, 269, 8737] C5 x C65
26) [10037, 3438, 385489] C5 x C65 14) [2281, 1719, 642368] C5 x C65
27) [10613, 1550, 430817] C5 x C65 ---) [233, 775, 42452] C65
28) [14281, 1658, 173125] C5 x C65 ---) [277, 829, 128529] C65
29) [18049, 5598, 614801] C5 x C65 ---) [5081, 2799, 1804900] C5 x C195
30) [19477, 141, 101] C5 x C65 ---) [101, 282, 19477] C65
31) [20389, 317, 20025] C5 x C65 ---) [89, 634, 20389] C65
32) [27893, 1357, 453389] C5 x C65 ---) [101, 1681, 697325] C65
33) [30341, 365, 25721] C5 x C65 ---) [89, 730, 30341] C65
34) [30893, 730, 9653] C5 x C65 ---) [197, 365, 30893] C65
35) [35509, 189, 53] C5 x C65 ---) [53, 378, 35509] C65
36) [38177, 1451, 287744] C5 x C65 ---) [281, 2902, 954425] C65
37) [53441, 271, 5000] C5 x C65 ---) [8, 542, 53441] C65
38) [55201, 237, 242] C5 x C65 ---) [8, 474, 55201] C65
39) [58657, 1519, 562176] C5 x C65 ---) [61, 1561, 527913] C65
40) [64333, 305, 7173] C5 x C65 7) [797, 610, 64333] C5 x C65
41) [85361, 319, 4100] C5 x C65 ---) [41, 638, 85361] C65
42) [95393, 415, 19208] C5 x C65 ---) [8, 830, 95393] C65
43) [128749, 1594, 120213] C5 x C65 ---) [37, 797, 128749] C65
44) [164149, 509, 23733] C5 x C65 4) [293, 1018, 164149] C5 x C65
45) [167597, 417, 1573] C5 x C65 ---) [13, 834, 167597] C65
46) [278329, 2059, 990288] C5 x C65 ---) [13, 1121, 278329] C65
47) [320141, 881, 114005] C5 x C65 ---) [5, 1133, 320141] C65
48) [351293, 593, 89] C5 x C65 3) [89, 1186, 351293] C5 x C65
49) [545033, 739, 272] C5 x C65 ---) [17, 1478, 545033] C65
50) [616789, 2633, 345397] C5 x C65 ---) [13, 1577, 616789] C65
51) [688889, 833, 1250] C5 x C65 ---) [8, 1666, 688889] C65
52) [876301, 3229, 634933] C5 x C65 2) [13, 1873, 876301] C5 x C65
53) [1882561, 1919, 450000] C5 x C65 1) [5, 2757, 1882561] C5 x C65