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 C6 x C30 non-normal (D4) quartic CM field invariants: 58 fields

K Quartic invariants Cl(OK) Igusa invariants Kr Reflex invariants Cl(OKr) Igusa invariants
1) [229, 657, 107397] C3 x C6 x C30 ---) [11933, 1314, 2061] C3 x C60
2) [257, 1654, 618137] C3 x C6 x C30 ---) [618137, 827, 16448] C3 x C12 x C120
3) [316, 2806, 1948185] C3 x C6 x C30 ---) [216465, 1403, 5056] C6 x C60
4) [316, 286, 15393] C3 x C6 x C30 ---) [15393, 143, 1264] C6 x C60
5) [316, 250, 2274] C3 x C6 x C30 ---) [9096, 500, 53404] C6 x C60
6) [321, 155, 5926] C3 x C6 x C30 ---) [23704, 310, 321] C6 x C30
7) [321, 1303, 347332] C3 x C6 x C30 ---) [86833, 2606, 308481] C3 x C60
8) [321, 1910, 398425] C3 x C6 x C30 ---) [15937, 955, 128400] C6 x C30
9) [469, 1033, 69675] C3 x C6 x C30 ---) [11148, 2066, 788389] C6 x C60
10) [469, 898, 109677] C3 x C6 x C30 ---) [109677, 449, 22981] C3 x C60
11) [473, 471, 54396] C3 x C6 x C30 ---) [6044, 942, 4257] C6 x C30
12) [568, 1222, 146121] C3 x C6 x C30 ---) [146121, 611, 56800] C6 x C60
13) [568, 666, 42161] C3 x C6 x C30 ---) [42161, 333, 17182] C3 x C6 x C180
14) [568, 650, 23833] C3 x C6 x C30 ---) [23833, 325, 20448] C6 x C30
15) [733, 610, 90093] C3 x C6 x C30 ---) [90093, 305, 733] C2 x C6 x C30
16) [785, 1258, 317141] C3 x C6 x C30 ---) [2621, 629, 19625] C3 x C30
17) [892, 286, 6177] C3 x C6 x C30 ---) [6177, 143, 3568] C6 x C60
18) [993, 503, 63004] C3 x C6 x C30 ---) [63004, 1006, 993] C2 x C6 x C30
19) [1436, 206, 1634] C3 x C6 x C30 ---) [6536, 412, 35900] C6 x C60
20) [1509, 434, 41053] C3 x C6 x C30 ---) [41053, 217, 1509] C2 x C30 x C30
21) [1901, 1338, 379125] C3 x C6 x C30 ---) [1685, 669, 17109] C2 x C6 x C30
22) [2713, 725, 98172] C3 x C6 x C30 ---) [1212, 1450, 132937] C6 x C60
23) [2777, 85, 1112] C3 x C6 x C30 ---) [1112, 170, 2777] C6 x C30
24) [2777, 489, 3546] C3 x C6 x C30 ---) [1576, 978, 224937] C6 x C60
25) [4481, 214, 6968] C3 x C6 x C30 ---) [6968, 428, 17924] C6 x C60
26) [5613, 367, 32269] C3 x C6 x C30 ---) [61, 543, 50517] C6 x C30
27) [7148, 1234, 266321] C3 x C6 x C30 ---) [2201, 617, 28592] C3 x C60
28) [7388, 694, 2201] C3 x C6 x C30 ---) [2201, 347, 29552] C3 x C60
29) [8572, 190, 453] C3 x C6 x C30 ---) [453, 95, 2143] C3 x C60
30) [11885, 442, 1301] C3 x C6 x C30 ---) [1301, 221, 11885] C3 x C30
31) [12248, 728, 22264] C3 x C6 x C30 ---) [184, 364, 27558] C3 x C60
32) [13269, 888, 144060] C3 x C6 x C30 ---) [60, 444, 13269] C6 x C60
33) [13589, 173, 4085] C3 x C6 x C30 ---) [4085, 346, 13589] C6 x C60
34) [15349, 143, 1275] C3 x C6 x C30 ---) [204, 286, 15349] C2 x C6 x C30
35) [16661, 478, 40460] C3 x C6 x C30 ---) [140, 956, 66644] C6 x C60
36) [20549, 1293, 1845] C3 x C6 x C30 ---) [205, 2586, 1664469] C6 x C60
37) [24952, 694, 20601] C3 x C6 x C30 ---) [2289, 347, 24952] C6 x C120
38) [28473, 1727, 681568] C3 x C6 x C30 ---) [472, 3454, 256257] C3 x C60
39) [29221, 382, 7260] C3 x C6 x C30 ---) [60, 764, 116884] C6 x C60
40) [32009, 253, 8000] C3 x C6 x C30 ---) [5, 359, 32009] C60
41) [32197, 2010, 881237] C3 x C6 x C30 ---) [917, 1005, 32197] C3 x C60
42) [37085, 193, 41] C3 x C6 x C30 ---) [41, 386, 37085] C3 x C30
43) [52149, 567, 67335] C3 x C6 x C30 ---) [60, 1134, 52149] C6 x C60
44) [57677, 241, 101] C3 x C6 x C30 ---) [101, 482, 57677] C3 x C30
45) [67313, 1342, 180989] C3 x C6 x C30 ---) [29, 671, 67313] C6 x C30
46) [80101, 301, 2625] C3 x C6 x C30 ---) [105, 602, 80101] C6 x C60
47) [97001, 461, 28880] C3 x C6 x C30 ---) [5, 623, 97001] C3 x C60
48) [104332, 2036, 97336] C3 x C6 x C30 ---) [184, 1018, 234747] C3 x C60
49) [105401, 325, 56] C3 x C6 x C30 ---) [56, 650, 105401] C6 x C30
50) [142616, 758, 1025] C3 x C6 x C30 ---) [41, 379, 35654] C6 x C30
51) [146161, 609, 56180] C3 x C6 x C30 ---) [5, 767, 146161] C3 x C60
52) [186401, 3454, 113] C3 x C6 x C30 ---) [113, 1727, 745604] C3 x C30
53) [196369, 445, 414] C3 x C6 x C30 ---) [184, 890, 196369] C3 x C60
54) [201129, 627, 48000] C3 x C6 x C30 ---) [120, 1254, 201129] C6 x C60
55) [264757, 1545, 1053] C3 x C6 x C30 ---) [13, 3090, 2382813] C6 x C30
56) [418469, 683, 12005] C3 x C6 x C30 ---) [5, 1366, 418469] C6 x C30
57) [698869, 973, 61965] C3 x C6 x C30 ---) [85, 1946, 698869] C2 x C6 x C30
58) [906601, 1171, 116160] C3 x C6 x C30 ---) [60, 2342, 906601] C6 x C60