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 C7 x C21 non-normal (D4) quartic CM field invariants: 39 fields

K Quartic invariants Cl(OK) Igusa invariants Kr Reflex invariants Cl(OKr) Igusa invariants
1) [5, 2666, 1736389] C7 x C21 36) [1736389, 1333, 10125] C7 x C21
2) [5, 3214, 2294449] C7 x C21 38) [2294449, 1607, 72000] C7 x C21
3) [5, 4509, 4296709] C7 x C21 39) [4296709, 4373, 3706605] C7 x C21
4) [8, 3122, 1721513] C7 x C21 35) [1721513, 1561, 178802] C7 x C21
5) [29, 869, 185593] C7 x C21 33) [185593, 1738, 12789] C7 x C21
6) [53, 577, 72089] C7 x C21 28) [72089, 1154, 44573] C7 x C21
7) [73, 3398, 2213833] C7 x C21 37) [2213833, 1699, 168192] C7 x C21
8) [97, 3526, 3083337] C7 x C21 ---) [342593, 1763, 6208] C7 x C105
9) [521, 742, 104297] C7 x C21 31) [104297, 371, 8336] C7 x C21
10) [541, 638, 23857] C7 x C21 ---) [23857, 319, 19476] C7 x C7 x C21
11) [577, 215, 11412] C7 x C21 ---) [317, 430, 577] C21
12) [613, 417, 17573] C7 x C21 25) [17573, 834, 103597] C7 x C21
13) [1009, 291, 14864] C7 x C21 ---) [929, 582, 25225] C21
14) [1601, 63, 592] C7 x C21 ---) [37, 126, 1601] C21
15) [1601, 151, 5300] C7 x C21 ---) [53, 281, 1601] C21
16) [1601, 559, 45700] C7 x C21 ---) [457, 807, 6404] C21
17) [2633, 3467, 866368] C7 x C21 ---) [13537, 5543, 7677828] C21 x C21
18) [3301, 4229, 4285429] C7 x C21 ---) [8101, 3169, 29709] C7 x C273
19) [3557, 1025, 254653] C7 x C21 20) [5197, 2050, 32013] C7 x C21
20) [5197, 2050, 32013] C7 x C21 19) [3557, 1025, 254653] C7 x C21
21) [5197, 3029, 1720741] C7 x C21 23) [14221, 6058, 2291877] C7 x C21
22) [5273, 739, 71936] C7 x C21 ---) [281, 1063, 21092] C21
23) [14221, 6058, 2291877] C7 x C21 21) [5197, 3029, 1720741] C7 x C21
24) [17569, 143, 720] C7 x C21 ---) [5, 286, 17569] C21
25) [17573, 834, 103597] C7 x C21 12) [613, 417, 17573] C7 x C21
26) [23629, 658, 13725] C7 x C21 ---) [61, 329, 23629] C21
27) [40093, 553, 66429] C7 x C21 ---) [61, 1106, 40093] C7 x C7
28) [72089, 1154, 44573] C7 x C21 6) [53, 577, 72089] C7 x C21
29) [80429, 353, 11045] C7 x C21 ---) [5, 589, 80429] C21
30) [98389, 333, 3125] C7 x C21 ---) [5, 666, 98389] C21
31) [104297, 371, 8336] C7 x C21 9) [521, 742, 104297] C7 x C21
32) [125029, 357, 605] C7 x C21 ---) [5, 714, 125029] C21
33) [185593, 1738, 12789] C7 x C21 5) [29, 869, 185593] C7 x C21
34) [254489, 763, 81920] C7 x C21 ---) [5, 1009, 254489] C7 x C7
35) [1721513, 1561, 178802] C7 x C21 4) [8, 3122, 1721513] C7 x C21
36) [1736389, 1333, 10125] C7 x C21 1) [5, 2666, 1736389] C7 x C21
37) [2213833, 1699, 168192] C7 x C21 7) [73, 3398, 2213833] C7 x C21
38) [2294449, 1607, 72000] C7 x C21 2) [5, 3214, 2294449] C7 x C21
39) [4296709, 4373, 3706605] C7 x C21 3) [5, 4509, 4296709] C7 x C21