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 C3 x C321 non-normal (D4) quartic CM field invariants: 65 fields

K Quartic invariants Cl(OK) Igusa invariants Kr Reflex invariants Cl(OKr) Igusa invariants
1) [13, 7182, 12545633] C3 x C321 64) [12545633, 3591, 87412] C3 x C321
2) [13, 10341, 26710589] C3 x C321 65) [26710589, 18373, 24292957] C3 x C321
3) [257, 1070, 23057] C3 x C321 ---) [23057, 535, 65792] C321
4) [257, 2134, 1122041] C3 x C321 ---) [1122041, 1067, 4112] C321
5) [353, 662, 103913] C3 x C321 40) [103913, 331, 1412] C3 x C321
6) [733, 633, 99989] C3 x C321 ---) [99989, 1266, 733] C321
7) [929, 1799, 585908] C3 x C321 42) [146477, 3598, 892769] C3 x C321
8) [2741, 6001, 8755625] C3 x C321 ---) [14009, 3695, 2148944] C3 x C3531
9) [3889, 5071, 4094388] C3 x C321 ---) [12637, 5521, 35001] C321
10) [3917, 6958, 3078673] C3 x C321 32) [18217, 3479, 2256192] C3 x C321
11) [4297, 1051, 189136] C3 x C321 ---) [11821, 2102, 348057] C3 x C3 x C321
12) [4597, 237, 12893] C3 x C321 ---) [12893, 474, 4597] C321
13) [4729, 1426, 338125] C3 x C321 ---) [541, 713, 42561] C321
14) [4933, 5762, 7806861] C3 x C321 ---) [10709, 2881, 123325] C321
15) [5281, 3882, 197525] C3 x C321 ---) [7901, 1941, 892489] C321
16) [5281, 1915, 693684] C3 x C321 ---) [2141, 3669, 3300625] C321
17) [5333, 3145, 7577] C3 x C321 ---) [7577, 6290, 9860717] C321
18) [5477, 2974, 1422481] C3 x C321 ---) [2689, 1487, 197172] C321
19) [5477, 3929, 13037] C3 x C321 ---) [13037, 7858, 15384893] C321
20) [5741, 137, 3257] C3 x C321 ---) [3257, 274, 5741] C321
21) [10733, 3857, 2299673] C3 x C321 ---) [2393, 3595, 42932] C321
22) [10889, 946, 180173] C3 x C321 ---) [3677, 473, 10889] C321
23) [11789, 4921, 1571293] C3 x C321 ---) [5437, 7401, 1426469] C321
24) [11821, 8917, 11576925] C3 x C321 ---) [5717, 5097, 6253309] C321
25) [12821, 4257, 142525] C3 x C321 ---) [5701, 8514, 17551949] C321
26) [12821, 677, 111377] C3 x C321 ---) [2273, 1354, 12821] C321
27) [13877, 6837, 1191661] C3 x C321 ---) [3301, 3773, 3122325] C321
28) [13877, 2005, 2393] C3 x C321 ---) [2393, 4010, 4010453] C321
29) [15641, 979, 235700] C3 x C321 ---) [2357, 1958, 15641] C321
30) [17053, 413, 4273] C3 x C321 ---) [4273, 826, 153477] C321
31) [17477, 8313, 11294989] C3 x C321 ---) [4021, 5181, 436925] C321
32) [18217, 3479, 2256192] C3 x C321 10) [3917, 6958, 3078673] C3 x C321
33) [18269, 4273, 4340837] C3 x C321 ---) [4517, 8546, 895181] C321
34) [18661, 4429, 2436093] C3 x C321 ---) [2237, 6801, 9871669] C321
35) [18701, 6018, 2797] C3 x C321 ---) [2797, 3009, 2262821] C321
36) [23917, 485, 4993] C3 x C321 ---) [4993, 970, 215253] C321
37) [24281, 1327, 385600] C3 x C321 ---) [241, 2654, 218529] C321
38) [35597, 1162, 195173] C3 x C321 ---) [1613, 581, 35597] C321
39) [41269, 2518, 924777] C3 x C321 ---) [233, 1259, 165076] C321
40) [103913, 331, 1412] C3 x C321 5) [353, 662, 103913] C3 x C321
41) [130369, 3559, 1569600] C3 x C321 ---) [109, 2197, 1173321] C321
42) [146477, 3598, 892769] C3 x C321 7) [929, 1799, 585908] C3 x C321
43) [146857, 2471, 1196032] C3 x C321 ---) [73, 3071, 2349712] C321
44) [171617, 1711, 688976] C3 x C321 ---) [149, 3422, 171617] C321
45) [211349, 493, 7925] C3 x C321 ---) [317, 986, 211349] C321
46) [241877, 493, 293] C3 x C321 ---) [293, 986, 241877] C321
47) [405037, 809, 62361] C3 x C321 ---) [41, 1618, 405037] C321
48) [572801, 927, 71632] C3 x C321 ---) [37, 1854, 572801] C321
49) [608393, 803, 9104] C3 x C321 ---) [569, 1606, 608393] C321
50) [827873, 911, 512] C3 x C321 ---) [8, 1822, 827873] C321
51) [920921, 987, 13312] C3 x C321 ---) [13, 1974, 920921] C321
52) [1023977, 1587, 373648] C3 x C321 ---) [193, 3174, 1023977] C321
53) [1226993, 1119, 6292] C3 x C321 ---) [13, 2238, 1226993] C321
54) [1484369, 1271, 32768] C3 x C321 ---) [8, 2542, 1484369] C321
55) [1535153, 1479, 163072] C3 x C321 ---) [13, 2958, 1535153] C321
56) [1918417, 1847, 373248] C3 x C321 ---) [8, 3694, 1918417] C321
57) [2851097, 1755, 57232] C3 x C321 ---) [73, 3510, 2851097] C321
58) [3960937, 2035, 45072] C3 x C321 ---) [313, 4070, 3960937] C321
59) [3974681, 2299, 327680] C3 x C321 ---) [5, 4337, 3974681] C321
60) [4431257, 2491, 443456] C3 x C321 ---) [41, 4982, 4431257] C321
61) [4884553, 2915, 903168] C3 x C321 ---) [8, 5830, 4884553] C321
62) [6914129, 2647, 23120] C3 x C321 ---) [5, 5294, 6914129] C321
63) [11380409, 3403, 50000] C3 x C321 ---) [5, 6806, 11380409] C321
64) [12545633, 3591, 87412] C3 x C321 1) [13, 7182, 12545633] C3 x C321
65) [26710589, 18373, 24292957] C3 x C321 2) [13, 10341, 26710589] C3 x C321