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 C165 non-normal (D4) quartic CM field invariants: 58 fields

K Quartic invariants Cl(OK) Igusa invariants Kr Reflex invariants Cl(OKr) Igusa invariants
1) [8, 4462, 4862161] C5 x C165 57) [4862161, 2231, 28800] C5 x C165
2) [37, 3558, 3162473] C5 x C165 55) [3162473, 1779, 592] C5 x C165
3) [401, 115, 2404] C5 x C165 ---) [601, 230, 3609] C165
4) [401, 770, 18301] C5 x C165 ---) [18301, 385, 32481] C165
5) [773, 1377, 404269] C5 x C165 44) [404269, 2754, 279053] C5 x C165
6) [1093, 210, 6653] C5 x C165 ---) [6653, 105, 1093] C165
7) [1429, 1230, 12401] C5 x C165 ---) [12401, 615, 91456] C3 x C165
8) [1429, 1041, 141953] C5 x C165 ---) [2897, 2011, 691636] C165
9) [1997, 933, 205141] C5 x C165 37) [205141, 1866, 49925] C5 x C165
10) [2153, 562, 1453] C5 x C165 ---) [1453, 281, 19377] C165
11) [2153, 226, 4157] C5 x C165 ---) [4157, 113, 2153] C165
12) [2153, 171, 6772] C5 x C165 ---) [1693, 342, 2153] C165
13) [4357, 622, 27009] C5 x C165 ---) [3001, 311, 17428] C165
14) [4493, 4430, 1383713] C5 x C165 ---) [3833, 2215, 880628] C5 x C55
15) [4889, 475, 55184] C5 x C165 ---) [3449, 950, 4889] C165
16) [6113, 2511, 621124] C5 x C165 ---) [3169, 3863, 1980612] C165
17) [6949, 1654, 239193] C5 x C165 ---) [2953, 827, 111184] C165
18) [7817, 1331, 284596] C5 x C165 ---) [421, 1589, 70353] C165
19) [12301, 546, 25325] C5 x C165 ---) [1013, 273, 12301] C165
20) [13229, 4249, 2446469] C5 x C165 ---) [2909, 5129, 13229] C165
21) [15121, 762, 84677] C5 x C165 ---) [293, 381, 15121] C165
22) [16001, 659, 8564] C5 x C165 ---) [2141, 1318, 400025] C165
23) [16001, 4563, 3761152] C5 x C165 ---) [3673, 8607, 18497156] C165
24) [16741, 4717, 5558337] C5 x C165 ---) [2137, 5263, 5424084] C165
25) [16741, 2357, 179325] C5 x C165 ---) [797, 3989, 16741] C165
26) [17033, 835, 170048] C5 x C165 ---) [2657, 1670, 17033] C165
27) [18433, 3451, 2862144] C5 x C165 ---) [4969, 6902, 460825] C165
28) [22129, 327, 21200] C5 x C165 ---) [53, 654, 22129] C5 x C15
29) [33029, 1709, 721913] C5 x C165 ---) [257, 3239, 2113856] C3 x C165
30) [33029, 373, 26525] C5 x C165 ---) [1061, 746, 33029] C165
31) [35933, 1385, 39377] C5 x C165 ---) [233, 2770, 1760717] C165
32) [37993, 3023, 679428] C5 x C165 ---) [233, 1563, 607888] C55
33) [52313, 954, 18277] C5 x C165 ---) [373, 477, 52313] C165
34) [126001, 2942, 147825] C5 x C165 ---) [73, 1471, 504004] C165
35) [143513, 699, 86272] C5 x C165 ---) [337, 1398, 143513] C165
36) [158189, 617, 55625] C5 x C165 ---) [89, 1234, 158189] C165
37) [205141, 1866, 49925] C5 x C165 9) [1997, 933, 205141] C5 x C165
38) [249317, 2138, 145493] C5 x C165 ---) [173, 1069, 249317] C165
39) [255961, 507, 272] C5 x C165 ---) [17, 1014, 255961] C55
40) [261577, 2327, 765184] C5 x C165 ---) [61, 3593, 261577] C165
41) [306689, 863, 109520] C5 x C165 ---) [5, 1109, 306689] C55
42) [329873, 581, 1922] C5 x C165 ---) [8, 1162, 329873] C165
43) [372461, 617, 2057] C5 x C165 ---) [17, 1234, 372461] C165
44) [404269, 2754, 279053] C5 x C165 5) [773, 1377, 404269] C5 x C165
45) [570613, 821, 25857] C5 x C165 ---) [17, 1642, 570613] C165
46) [585677, 769, 1421] C5 x C165 ---) [29, 1538, 585677] C165
47) [673069, 1217, 202005] C5 x C165 ---) [5, 1641, 673069] C55
48) [859561, 3667, 3146832] C5 x C165 ---) [13, 1961, 859561] C165
49) [980081, 991, 500] C5 x C165 ---) [5, 1982, 980081] C165
50) [1227929, 1211, 59648] C5 x C165 ---) [233, 2422, 1227929] C5 x C55
51) [2112569, 1963, 435200] C5 x C165 ---) [17, 3926, 2112569] C165
52) [2225833, 4487, 25168] C5 x C165 ---) [13, 3617, 2225833] C165
53) [2812421, 2101, 400445] C5 x C165 ---) [5, 3473, 2812421] C165
54) [3157657, 2587, 883728] C5 x C165 ---) [17, 5174, 3157657] C165
55) [3162473, 1779, 592] C5 x C165 2) [37, 3558, 3162473] C5 x C165
56) [4169609, 2051, 9248] C5 x C165 ---) [8, 4102, 4169609] C165
57) [4862161, 2231, 28800] C5 x C165 1) [8, 4462, 4862161] C5 x C165
58) [8077529, 2843, 1280] C5 x C165 ---) [5, 5686, 8077529] C5 x C55