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 C12 x C36 non-normal (D4) quartic CM field invariants: 637 fields

K Quartic invariants Cl(OK) Igusa invariants Kr Reflex invariants Cl(OKr) Igusa invariants
1) [5, 1082, 291961] C12 x C36 ---) [291961, 541, 180] C2 x C12 x C36
2) [5, 1898, 899996] C12 x C36 ---) [899996, 1396, 262205] C2 x C12 x C72
3) [5, 6025, 8064905] C12 x C36 ---) [8064905, 3395, 865280] C4 x C12 x C144
4) [5, 1899, 899649] C12 x C36 ---) [99961, 1473, 317520] C2 x C6 x C6 x C18
5) [5, 7510, 14099705] C12 x C36 ---) [14099705, 3755, 80] C2 x C2 x C12 x C72
6) [13, 2809, 1972357] C12 x C36 ---) [1972357, 4945, 1675453] C24 x C72
7) [17, 8870, 19651817] C12 x C36 ---) [19651817, 4435, 4352] C4 x C12 x C36
8) [21, 3910, 3819001] C12 x C36 ---) [3819001, 1955, 756] C2 x C12 x C72
9) [28, 1012, 253768] C12 x C36 ---) [253768, 506, 567] C2 x C12 x C36
10) [37, 3294, 2248481] C12 x C36 ---) [2248481, 1647, 116032] C2 x C12 x C72
11) [37, 4881, 5904009] C12 x C36 ---) [72889, 2499, 85248] C6 x C72
12) [37, 6006, 8932761] C12 x C36 ---) [110281, 3003, 21312] C6 x C72
13) [40, 644, 65244] C12 x C36 ---) [65244, 322, 9610] C3 x C18 x C72
14) [40, 2550, 701465] C12 x C36 610) [701465, 1275, 231040] C12 x C36
15) [40, 516, 29354] C12 x C36 ---) [117416, 1032, 148840] C12 x C72
16) [40, 482, 13191] C12 x C36 ---) [52764, 694, 1690] C3 x C12 x C36
17) [40, 1112, 308776] C12 x C36 ---) [308776, 556, 90] C12 x C72
18) [40, 660, 29690] C12 x C36 ---) [118760, 1060, 13690] C2 x C12 x C72
19) [40, 448, 41766] C12 x C36 ---) [167064, 896, 33640] C2 x C6 x C144
20) [40, 358, 31791] C12 x C36 ---) [127164, 716, 1000] C6 x C72
21) [40, 556, 71034] C12 x C36 589) [284136, 1112, 25000] C12 x C36
22) [40, 4310, 3947065] C12 x C36 634) [3947065, 2155, 174240] C12 x C36
23) [40, 1036, 253884] C12 x C36 ---) [253884, 518, 3610] C6 x C72
24) [40, 1306, 326409] C12 x C36 ---) [326409, 653, 25000] C6 x C36
25) [40, 688, 111576] C12 x C36 ---) [111576, 344, 1690] C6 x C72
26) [56, 534, 63883] C12 x C36 ---) [255532, 1068, 29624] C2 x C2 x C6 x C144
27) [60, 338, 28426] C12 x C36 ---) [113704, 676, 540] C2 x C12 x C252
28) [60, 430, 38965] C12 x C36 459) [38965, 215, 1815] C12 x C36
29) [60, 2706, 1761249] C12 x C36 ---) [1761249, 1353, 17340] C2 x C6 x C1368
30) [60, 308, 23341] C12 x C36 ---) [23341, 616, 1500] C12 x C180
31) [60, 890, 168985] C12 x C36 564) [168985, 445, 7260] C12 x C36
32) [60, 3174, 2503209] C12 x C36 ---) [2503209, 1587, 3840] C2 x C6 x C36
33) [60, 1910, 834265] C12 x C36 614) [834265, 955, 19440] C12 x C36
34) [60, 412, 41896] C12 x C36 466) [41896, 206, 135] C12 x C36
35) [60, 5046, 2433369] C12 x C36 ---) [2433369, 2523, 983040] C3 x C18 x C324
36) [60, 1460, 271540] C12 x C36 504) [67885, 730, 65340] C12 x C36
37) [60, 2754, 121089] C12 x C36 ---) [121089, 1377, 443760] C2 x C6 x C144
38) [65, 2710, 1769465] C12 x C36 631) [1769465, 1355, 16640] C12 x C36
39) [77, 327, 21169] C12 x C36 ---) [21169, 654, 22253] C2 x C6 x C36
40) [85, 356, 9924] C12 x C36 ---) [2481, 178, 5440] C2 x C6 x C18
41) [85, 1957, 165921] C12 x C36 ---) [165921, 3914, 3166165] C2 x C6 x C36
42) [88, 1342, 309441] C12 x C36 ---) [309441, 671, 35200] C2 x C12 x C36
43) [104, 1094, 228905] C12 x C36 ---) [228905, 547, 17576] C6 x C6 x C72
44) [104, 1522, 465865] C12 x C36 ---) [465865, 761, 28314] C3 x C6 x C72
45) [104, 1252, 121372] C12 x C36 ---) [121372, 626, 67626] C6 x C72
46) [105, 2406, 1279209] C12 x C36 ---) [1279209, 1203, 42000] C2 x C6 x C144
47) [113, 682, 114473] C12 x C36 ---) [114473, 341, 452] C6 x C72
48) [120, 2022, 530601] C12 x C36 ---) [530601, 1011, 122880] C2 x C6 x C36
49) [120, 434, 25219] C12 x C36 ---) [100876, 868, 87480] C6 x C36
50) [136, 1174, 342393] C12 x C36 ---) [342393, 587, 544] C12 x C72
51) [136, 346, 27175] C12 x C36 ---) [4348, 214, 1666] C6 x C252
52) [136, 496, 61368] C12 x C36 ---) [61368, 248, 34] C6 x C72
53) [136, 4270, 3505041] C12 x C36 ---) [389449, 2135, 263296] C6 x C36
54) [137, 717, 70948] C12 x C36 ---) [17737, 1434, 230297] C3 x C6 x C360
55) [145, 1583, 626436] C12 x C36 ---) [17401, 1451, 522000] C3 x C36
56) [156, 404, 34213] C12 x C36 ---) [34213, 808, 26364] C6 x C36
57) [165, 1718, 62041] C12 x C36 ---) [62041, 859, 168960] C3 x C6 x C36
58) [165, 1898, 419461] C12 x C36 ---) [419461, 949, 120285] C2 x C6 x C36
59) [168, 2262, 752313] C12 x C36 ---) [752313, 1131, 131712] C2 x C6 x C180
60) [168, 790, 155353] C12 x C36 ---) [155353, 395, 168] C2 x C6 x C36
61) [168, 1734, 186537] C12 x C36 ---) [186537, 867, 141288] C2 x C6 x C72
62) [184, 1036, 263724] C12 x C36 ---) [263724, 518, 1150] C2 x C6 x C72
63) [193, 3990, 1559033] C12 x C36 ---) [31817, 1995, 605248] C6 x C72
64) [204, 7430, 13719625] C12 x C36 ---) [548785, 3715, 20400] C2 x C12 x C36
65) [204, 1502, 556657] C12 x C36 605) [556657, 751, 1836] C12 x C36
66) [204, 2486, 810649] C12 x C36 ---) [810649, 1243, 183600] C6 x C36
67) [220, 1350, 441545] C12 x C36 ---) [441545, 675, 3520] C2 x C12 x C36
68) [220, 4710, 5514345] C12 x C36 ---) [612705, 2355, 7920] C2 x C6 x C36
69) [229, 757, 143205] C12 x C36 ---) [143205, 1514, 229] C4 x C72
70) [229, 1397, 199305] C12 x C36 ---) [22145, 1851, 718144] C4 x C72
71) [229, 633, 93245] C12 x C36 ---) [93245, 1266, 27709] C8 x C72
72) [232, 2734, 1141137] C12 x C36 ---) [126793, 1367, 181888] C6 x C36
73) [248, 800, 159752] C12 x C36 ---) [159752, 400, 62] C2 x C6 x C72
74) [257, 336, 2524] C12 x C36 ---) [2524, 168, 6425] C4 x C36
75) [257, 119, 1934] C12 x C36 ---) [7736, 238, 6425] C4 x C252
76) [257, 394, 1801] C12 x C36 ---) [1801, 197, 9252] C2 x C72
77) [265, 486, 58784] C12 x C36 ---) [14696, 972, 1060] C6 x C72
78) [268, 3334, 2504457] C12 x C36 ---) [278273, 1667, 68608] C2 x C12 x C72
79) [285, 240, 11835] C12 x C36 ---) [5260, 480, 10260] C2 x C6 x C36
80) [305, 178, 5176] C12 x C36 ---) [5176, 356, 10980] C6 x C252
81) [305, 709, 121934] C12 x C36 ---) [487736, 1418, 14945] C6 x C72
82) [305, 1623, 652356] C12 x C36 ---) [18121, 3246, 24705] C2 x C6 x C18
83) [305, 437, 45836] C12 x C36 475) [45836, 874, 7625] C12 x C36
84) [312, 648, 14808] C12 x C36 ---) [14808, 324, 22542] C2 x C6 x C36
85) [313, 445, 36282] C12 x C36 ---) [145128, 890, 52897] C12 x C72
86) [316, 4390, 1658025] C12 x C36 ---) [7369, 2195, 790000] C2 x C2 x C36
87) [316, 3254, 2601625] C12 x C36 ---) [104065, 1627, 11376] C2 x C4 x C72
88) [321, 4710, 286761] C12 x C36 ---) [286761, 2355, 1314816] C2 x C2 x C4 x C252
89) [328, 1010, 228457] C12 x C36 ---) [228457, 505, 6642] C3 x C3 x C36
90) [328, 1982, 25633] C12 x C36 ---) [25633, 991, 239112] C3 x C36
91) [345, 1694, 711889] C12 x C36 ---) [711889, 847, 1380] C3 x C18 x C36
92) [348, 304, 22756] C12 x C36 ---) [5689, 152, 87] C6 x C36
93) [353, 1433, 246416] C12 x C36 394) [15401, 2377, 22592] C12 x C36
94) [353, 1153, 120464] C12 x C36 ---) [7529, 1477, 1412] C6 x C72
95) [357, 2030, 64897] C12 x C36 ---) [64897, 1015, 241332] C2 x C6 x C36
96) [365, 732, 2191] C12 x C36 362) [8764, 1464, 527060] C12 x C36
97) [365, 199, 9809] C12 x C36 ---) [9809, 398, 365] C2 x C6 x C36
98) [365, 653, 73661] C12 x C36 ---) [73661, 1306, 131765] C3 x C6 x C72
99) [377, 1868, 39563] C12 x C36 ---) [158252, 3736, 3331172] C3 x C72
100) [377, 2252, 43003] C12 x C36 ---) [172012, 4504, 4899492] C3 x C72
101) [380, 682, 91961] C12 x C36 ---)