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 C135 non-normal (D4) quartic CM field invariants: 55 fields

K Quartic invariants Cl(OK) Igusa invariants Kr Reflex invariants Cl(OKr) Igusa invariants
1) [53, 2494, 1432897] C5 x C135 ---) [1432897, 1247, 30528] C5 x C5 x C135
2) [157, 1237, 382189] C5 x C135 ---) [382189, 2474, 1413] C15 x C135
3) [317, 3214, 553649] C5 x C135 44) [553649, 1607, 507200] C5 x C135
4) [349, 894, 177473] C5 x C135 ---) [177473, 447, 5584] C15 x C135
5) [401, 742, 111977] C5 x C135 ---) [111977, 371, 6416] C135
6) [401, 475, 55504] C5 x C135 ---) [3469, 950, 3609] C135
7) [1429, 2241, 11933] C5 x C135 ---) [11933, 3913, 3156661] C135
8) [1429, 786, 11549] C5 x C135 ---) [11549, 393, 35725] C135
9) [1429, 1493, 168217] C5 x C135 ---) [3433, 1723, 205776] C135
10) [2081, 295, 21236] C5 x C135 ---) [5309, 590, 2081] C135
11) [2153, 2347, 1333504] C5 x C135 ---) [5209, 2907, 861200] C135
12) [2161, 1067, 46372] C5 x C135 28) [11593, 2134, 953001] C5 x C135
13) [2633, 330, 16693] C5 x C135 31) [16693, 165, 2633] C5 x C135
14) [2909, 2921, 2074153] C5 x C135 21) [7177, 3579, 186176] C5 x C135
15) [3181, 3309, 1763189] C5 x C135 ---) [6101, 3117, 1988125] C135
16) [3701, 3545, 3133429] C5 x C135 ---) [18541, 7090, 33309] C15 x C135
17) [4357, 481, 48037] C5 x C135 ---) [397, 962, 39213] C135
18) [4889, 3015, 599296] C5 x C135 ---) [2341, 3313, 1100025] C135
19) [4889, 1418, 483125] C5 x C135 ---) [773, 709, 4889] C135
20) [6949, 605, 6381] C5 x C135 ---) [709, 1210, 340501] C135
21) [7177, 3579, 186176] C5 x C135 14) [2909, 2921, 2074153] C5 x C135
22) [7213, 477, 11801] C5 x C135 29) [11801, 954, 180325] C5 x C135
23) [7229, 1053, 58525] C5 x C135 ---) [2341, 2106, 874709] C135
24) [7817, 1055, 41792] C5 x C135 ---) [653, 2110, 945857] C135
25) [8501, 1761, 416113] C5 x C135 ---) [433, 1139, 306036] C135
26) [9181, 1365, 188081] C5 x C135 ---) [521, 1923, 918100] C135
27) [10909, 297, 19325] C5 x C135 ---) [773, 594, 10909] C135
28) [11593, 2134, 953001] C5 x C135 12) [2161, 1067, 46372] C5 x C135
29) [11801, 954, 180325] C5 x C135 22) [7213, 477, 11801] C5 x C135
30) [15889, 2070, 54329] C5 x C135 ---) [449, 1035, 254224] C135
31) [16693, 165, 2633] C5 x C135 13) [2633, 330, 16693] C5 x C135
32) [16741, 2777, 1823301] C5 x C135 ---) [701, 3365, 2829229] C135
33) [18353, 5027, 36368] C5 x C135 ---) [2273, 6611, 1174592] C135
34) [23173, 1678, 333153] C5 x C135 ---) [457, 839, 92692] C135
35) [25153, 1151, 23076] C5 x C135 ---) [641, 2302, 1232497] C135
36) [30341, 970, 113861] C5 x C135 ---) [941, 485, 30341] C135
37) [46337, 1790, 59633] C5 x C135 ---) [1217, 895, 185348] C135
38) [74093, 273, 109] C5 x C135 ---) [109, 546, 74093] C135
39) [78713, 651, 86272] C5 x C135 ---) [337, 1302, 78713] C135
40) [83341, 2034, 700925] C5 x C135 ---) [53, 1017, 83341] C135
41) [158161, 1211, 10768] C5 x C135 ---) [673, 2422, 1423449] C135
42) [403097, 795, 57232] C5 x C135 ---) [73, 1590, 403097] C135
43) [444113, 679, 4232] C5 x C135 ---) [8, 1358, 444113] C135
44) [553649, 1607, 507200] C5 x C135 3) [317, 3214, 553649] C5 x C135
45) [642281, 851, 20480] C5 x C135 ---) [5, 1702, 642281] C135
46) [945397, 973, 333] C5 x C135 ---) [37, 1946, 945397] C135
47) [965233, 991, 4212] C5 x C135 ---) [13, 1982, 965233] C135
48) [1547501, 1249, 3125] C5 x C135 ---) [5, 2498, 1547501] C135
49) [1618217, 1273, 578] C5 x C135 ---) [8, 2546, 1618217] C135
50) [2213389, 2337, 812045] C5 x C135 ---) [5, 2981, 2213389] C135
51) [2223497, 1603, 86528] C5 x C135 ---) [8, 3206, 2223497] C135
52) [2984953, 2059, 313632] C5 x C135 ---) [8, 4118, 2984953] C135
53) [3053389, 2337, 602045] C5 x C135 ---) [5, 3541, 3053389] C135
54) [3265817, 1915, 100352] C5 x C135 ---) [8, 3830, 3265817] C135
55) [4837309, 3033, 1090445] C5 x C135 ---) [5, 4429, 4837309] C135