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 C9 x C36 non-normal (D4) quartic CM field invariants: 64 fields

K Quartic invariants Cl(OK) Igusa invariants Kr Reflex invariants Cl(OKr) Igusa invariants
1) [5, 1204, 336484] C9 x C36 ---) [84121, 602, 6480] C18 x C18
2) [8, 2462, 1077313] C9 x C36 58) [1077313, 1231, 109512] C9 x C36
3) [13, 792, 129308] C9 x C36 50) [129308, 396, 6877] C9 x C36
4) [28, 2762, 1680361] C9 x C36 61) [1680361, 1381, 56700] C9 x C36
5) [29, 420, 39199] C9 x C36 51) [156796, 840, 19604] C9 x C36
6) [37, 1398, 486233] C9 x C36 54) [486233, 699, 592] C9 x C36
7) [40, 2126, 300529] C9 x C36 ---) [300529, 1063, 207360] C9 x C252
8) [56, 3814, 2539049] C9 x C36 62) [2539049, 1907, 274400] C9 x C36
9) [56, 2678, 986521] C9 x C36 ---) [986521, 1339, 201600] C18 x C18
10) [61, 2726, 1427353] C9 x C36 59) [1427353, 1363, 107604] C9 x C36
11) [141, 2165, 1040641] C9 x C36 ---) [1040641, 4330, 524661] C18 x C18
12) [177, 4070, 3416233] C9 x C36 ---) [3416233, 2035, 181248] C18 x C18
13) [284, 516, 22189] C9 x C36 36) [22189, 1032, 177500] C9 x C36
14) [524, 670, 110129] C9 x C36 47) [110129, 335, 524] C9 x C36
15) [557, 934, 75497] C9 x C36 ---) [75497, 467, 35648] C18 x C36
16) [573, 149, 5407] C9 x C36 ---) [21628, 298, 573] C18 x C18
17) [1129, 983, 117100] C9 x C36 ---) [4684, 1966, 497889] C3 x C36
18) [1293, 121, 751] C9 x C36 ---) [3004, 242, 11637] C18 x C18
19) [1293, 327, 23823] C9 x C36 ---) [10588, 654, 11637] C18 x C18
20) [1916, 2030, 16661] C9 x C36 ---) [16661, 1015, 253391] C3 x C9 x C36
21) [2189, 293, 16537] C9 x C36 ---) [16537, 586, 19701] C18 x C18
22) [3085, 749, 9909] C9 x C36 ---) [1101, 1498, 521365] C3 x C9 x C18
23) [3469, 1018, 245205] C9 x C36 ---) [27245, 509, 3469] C3 x C18 x C36
24) [4409, 144, 775] C9 x C36 ---) [124, 288, 17636] C36
25) [5441, 703, 13372] C9 x C36 32) [13372, 1406, 440721] C9 x C36
26) [6616, 982, 135225] C9 x C36 ---) [601, 491, 26464] C36
27) [6616, 334, 1425] C9 x C36 ---) [57, 167, 6616] C2 x C18
28) [6809, 338, 1325] C9 x C36 ---) [53, 169, 6809] C36
29) [7465, 259, 14904] C9 x C36 ---) [184, 518, 7465] C18
30) [7541, 439, 1049] C9 x C36 ---) [1049, 878, 188525] C18 x C18
31) [11641, 155, 3096] C9 x C36 ---) [344, 310, 11641] C2 x C18
32) [13372, 1406, 440721] C9 x C36 25) [5441, 703, 13372] C9 x C36
33) [17133, 153, 1569] C9 x C36 ---) [1569, 306, 17133] C18 x C18
34) [17273, 299, 18032] C9 x C36 ---) [92, 598, 17273] C2 x C18
35) [21289, 691, 114048] C9 x C36 ---) [88, 1382, 21289] C18
36) [22189, 1032, 177500] C9 x C36 13) [284, 516, 22189] C9 x C36
37) [22492, 394, 16317] C9 x C36 ---) [37, 197, 5623] C36
38) [25177, 187, 2448] C9 x C36 ---) [17, 374, 25177] C18
39) [25361, 169, 800] C9 x C36 ---) [8, 338, 25361] C2 x C18
40) [38917, 874, 35301] C9 x C36 ---) [21, 437, 38917] C36
41) [48121, 715, 115776] C9 x C36 ---) [201, 1430, 48121] C36
42) [51809, 271, 5408] C9 x C36 ---) [8, 542, 51809] C36
43) [52753, 466, 1536] C9 x C36 ---) [24, 932, 211012] C2 x C18
44) [54584, 468, 172] C9 x C36 ---) [172, 234, 13646] C18 x C18
45) [56636, 482, 1445] C9 x C36 ---) [5, 241, 14159] C36
46) [71297, 703, 105728] C9 x C36 ---) [413, 1406, 71297] C18 x C18
47) [110129, 335, 524] C9 x C36 14) [524, 670, 110129] C9 x C36
48) [118873, 834, 55016] C9 x C36 ---) [104, 1668, 475492] C9 x C72
49) [124289, 703, 92480] C9 x C36 ---) [5, 749, 124289] C36
50) [129308, 396, 6877] C9 x C36 3) [13, 792, 129308] C9 x C36
51) [156796, 840, 19604] C9 x C36 5) [29, 420, 39199] C9 x C36
52) [193829, 677, 66125] C9 x C36 ---) [5, 881, 193829] C36
53) [281789, 697, 51005] C9 x C36 ---) [5, 1081, 281789] C36
54) [486233, 699, 592] C9 x C36 6) [37, 1398, 486233] C9 x C36
55) [487393, 721, 8112] C9 x C36 ---) [12, 1442, 487393] C2 x C18
56) [573361, 3243, 1339200] C9 x C36 ---) [93, 6486, 5160249] C18 x C18
57) [856129, 1177, 132300] C9 x C36 ---) [12, 2354, 856129] C18 x C18
58) [1077313, 1231, 109512] C9 x C36 2) [8, 2462, 1077313] C9 x C36
59) [1427353, 1363, 107604] C9 x C36 10) [61, 2726, 1427353] C9 x C36
60) [1536001, 1399, 105300] C9 x C36 ---) [13, 2798, 1536001] C9 x C18
61) [1680361, 1381, 56700] C9 x C36 4) [28, 2762, 1680361] C9 x C36
62) [2539049, 1907, 274400] C9 x C36 8) [56, 3814, 2539049] C9 x C36
63) [4256521, 2435, 418176] C9 x C36 ---) [24, 4870, 4256521] C18 x C18
64) [15680617, 4243, 580608] C9 x C36 ---) [28, 8486, 15680617] C18 x C18