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 C75 non-normal (D4) quartic CM field invariants: 90 fields

K Quartic invariants Cl(OK) Igusa invariants Kr Reflex invariants Cl(OKr) Igusa invariants
1) [5, 5369, 6008489] C5 x C75 88) [6008489, 2803, 462080] C5 x C75
2) [5, 4502, 5041081] C5 x C75 ---) [5041081, 2251, 6480] C15 x C75
3) [8, 2510, 1574737] C5 x C75 ---) [1574737, 1255, 72] C5 x C525
4) [13, 7934, 8069377] C5 x C75 89) [8069377, 3967, 1916928] C5 x C75
5) [17, 6326, 8890457] C5 x C75 90) [8890457, 3163, 278528] C5 x C75
6) [17, 1238, 304553] C5 x C75 73) [304553, 619, 19652] C5 x C75
7) [41, 1262, 80657] C5 x C75 ---) [80657, 631, 79376] C5 x C25 x C75
8) [53, 1582, 612113] C5 x C75 80) [612113, 791, 3392] C5 x C75
9) [97, 1927, 744784] C5 x C75 59) [46549, 1493, 545625] C5 x C75
10) [113, 1850, 363397] C5 x C75 ---) [363397, 925, 123057] C3 x C15 x C75
11) [317, 1850, 793493] C5 x C75 ---) [793493, 925, 15533] C5 x C5 x C75
12) [401, 1090, 295421] C5 x C75 ---) [6029, 545, 401] C75
13) [401, 255, 11344] C5 x C75 ---) [709, 510, 19649] C75
14) [401, 1135, 321956] C5 x C75 ---) [80489, 2270, 401] C75
15) [401, 3142, 1544137] C5 x C75 ---) [31513, 1571, 230976] C3 x C75
16) [677, 685, 109013] C5 x C75 66) [109013, 1370, 33173] C5 x C75
17) [1093, 1405, 34173] C5 x C75 ---) [3797, 1665, 578197] C75
18) [1093, 1021, 89829] C5 x C75 ---) [1109, 1009, 132253] C75
19) [1093, 1489, 49041] C5 x C75 ---) [5449, 2611, 983700] C75
20) [1429, 653, 3357] C5 x C75 ---) [373, 713, 12861] C75
21) [2081, 259, 3764] C5 x C75 ---) [941, 518, 52025] C75
22) [2081, 446, 16433] C5 x C75 ---) [16433, 223, 8324] C75
23) [3121, 498, 49517] C5 x C75 ---) [293, 249, 3121] C75
24) [3701, 2133, 559141] C5 x C75 32) [4621, 4137, 3556661] C5 x C75
25) [3833, 1903, 559424] C5 x C75 37) [8741, 3806, 1383713] C5 x C75
26) [4021, 733, 133317] C5 x C75 45) [14813, 1466, 4021] C5 x C75
27) [4273, 7111, 2590416] C5 x C75 ---) [17989, 8053, 8652825] C15 x C225
28) [4357, 745, 6957] C5 x C75 ---) [773, 1490, 527197] C75
29) [4357, 418, 26253] C5 x C75 ---) [2917, 209, 4357] C3 x C75
30) [4357, 1946, 511029] C5 x C75 ---) [701, 973, 108925] C75
31) [4441, 1731, 55184] C5 x C75 ---) [3449, 3462, 2775625] C75
32) [4621, 4137, 3556661] C5 x C75 24) [3701, 2133, 559141] C5 x C75
33) [4889, 2267, 1283600] C5 x C75 ---) [3209, 3623, 488900] C75
34) [5693, 6869, 9857] C5 x C75 40) [9857, 6227, 1115828] C5 x C75
35) [7229, 1426, 248125] C5 x C75 ---) [397, 713, 65061] C75
36) [8689, 707, 105412] C5 x C75 ---) [73, 767, 139024] C75
37) [8741, 3806, 1383713] C5 x C75 25) [3833, 1903, 559424] C5 x C75
38) [9181, 1965, 136721] C5 x C75 ---) [809, 2743, 918100] C75
39) [9181, 2665, 1773261] C5 x C75 ---) [4021, 5330, 9181] C75
40) [9857, 6227, 1115828] C5 x C75 34) [5693, 6869, 9857] C5 x C75
41) [10909, 2333, 1030725] C5 x C75 ---) [509, 1257, 272725] C75
42) [11273, 603, 88084] C5 x C75 ---) [61, 713, 101457] C75
43) [12301, 509, 37093] C5 x C75 ---) [757, 1018, 110709] C75
44) [13841, 1775, 784196] C5 x C75 ---) [4001, 3550, 13841] C3 x C75
45) [14813, 1466, 4021] C5 x C75 26) [4021, 733, 133317] C5 x C75
46) [15121, 3963, 747152] C5 x C75 ---) [953, 1987, 967744] C75
47) [15889, 827, 135232] C5 x C75 ---) [2113, 1654, 143001] C75
48) [15889, 399, 35828] C5 x C75 ---) [53, 798, 15889] C75
49) [18353, 1947, 172288] C5 x C75 ---) [673, 3535, 660708] C75
50) [18433, 2622, 1423793] C5 x C75 ---) [593, 1311, 73732] C75
51) [21317, 1834, 755621] C5 x C75 ---) [269, 917, 21317] C75
52) [27689, 203, 3380] C5 x C75 ---) [5, 349, 27689] C15
53) [27689, 179, 1088] C5 x C75 ---) [17, 358, 27689] C15
54) [27749, 850, 69629] C5 x C75 ---) [29, 425, 27749] C75
55) [30949, 293, 13725] C5 x C75 ---) [61, 586, 30949] C75
56) [35509, 205, 1629] C5 x C75 ---) [181, 410, 35509] C75
57) [36929, 1934, 344225] C5 x C75 ---) [281, 967, 147716] C75
58) [43889, 383, 25700] C5 x C75 ---) [257, 766, 43889] C3 x C75
59) [46549, 1493, 545625] C5 x C75 9) [97, 1927, 744784] C5 x C75
60) [46933, 221, 477] C5 x C75 ---) [53, 442, 46933] C75
61) [47857, 245, 3042] C5 x C75 ---) [8, 490, 47857] C75
62) [50909, 677, 37] C5 x C75 ---) [37, 1354, 458181] C75
63) [51257, 257, 3698] C5 x C75 ---) [8, 514, 51257] C25
64) [69193, 291, 3872] C5 x C75 ---) [8, 582, 69193] C25
65) [90481, 2414, 9153] C5 x C75 ---) [113, 1207, 361924] C75
66) [109013, 1370, 33173] C5 x C75 16) [677, 685, 109013] C5 x C75
67) [133033, 2875, 436752] C5 x C75 ---) [337, 5750, 6518617] C75
68) [137993, 1155, 299008] C5 x C75 ---) [73, 2310, 137993] C75
69) [174197, 517, 23273] C5 x C75 ---) [17, 1034, 174197] C75
70) [202361, 619, 45200] C5 x C75 ---) [113, 1238, 202361] C75
71) [261577, 1315, 366912] C5 x C75 ---) [13, 1361, 261577] C75
72) [286129, 703, 52020] C5 x C75 ---) [5, 1089, 286129] C75
73) [304553, 619, 19652] C5 x C75 6) [17, 1238, 304553] C5 x C75
74) [331153, 1787, 53248] C5 x C75 ---) [13, 1205, 331153] C75
75) [369673, 819, 75272] C5 x C75 ---) [8, 1638, 369673] C75
76) [409777, 1931, 10192] C5 x C75 ---) [13, 1421, 409777] C75
77) [413689, 891, 95048] C5 x C75 ---) [8, 1782, 413689] C75
78) [422969, 779, 45968] C5 x C75 ---) [17, 1558, 422969] C75
79) [531701, 941, 88445] C5 x C75 ---) [5, 1493, 531701] C75
80) [612113, 791, 3392] C5 x C75 8) [53, 1582, 612113] C5 x C75
81) [626617, 795, 1352] C5 x C75 ---) [8, 1590, 626617] C75
82) [755869, 1257, 206045] C5 x C75 ---) [5, 1741, 755869] C75
83) [772649, 907, 12500] C5 x C75 ---) [5, 1814, 772649] C75
84) [797009, 983, 42320] C5 x C75 ---) [5, 1966, 797009] C75
85) [959449, 1179, 107648] C5 x C75 ---) [8, 2358, 959449] C75
86) [1065469, 1033, 405] C5 x C75 ---) [5, 2066, 1065469] C75
87) [1566749, 2057, 666125] C5 x C75 ---) [5, 2521, 1566749] C75
88) [6008489, 2803, 462080] C5 x C75 1) [5, 5369, 6008489] C5 x C75
89) [8069377, 3967, 1916928] C5 x C75 4) [13, 7934, 8069377] C5 x C75
90) [8890457, 3163, 278528] C5 x C75 5) [17, 6326, 8890457] C5 x C75