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 C45 non-normal (D4) quartic CM field invariants: 71 fields

K Quartic invariants Cl(OK) Igusa invariants Kr Reflex invariants Cl(OKr) Igusa invariants
1) [5, 4337, 4589141] C5 x C45 70) [4589141, 3629, 2145125] C5 x C45
2) [8, 3878, 3655753] C5 x C45 ---) [3655753, 1939, 25992] C5 x C5 x C45
3) [8, 5110, 6441497] C5 x C45 71) [6441497, 2555, 21632] C5 x C45
4) [17, 8758, 18897113] C5 x C45 ---) [18897113, 4379, 69632] C15 x C45
5) [17, 1778, 652621] C5 x C45 ---) [652621, 889, 34425] C5 x C5 x C45
6) [53, 1214, 354881] C5 x C45 67) [354881, 607, 3392] C5 x C45
7) [53, 889, 195977] C5 x C45 58) [195977, 1778, 6413] C5 x C45
8) [61, 1069, 199909] C5 x C45 59) [199909, 2138, 343125] C5 x C45
9) [113, 2806, 550937] C5 x C45 ---) [550937, 1403, 354368] C15 x C45
10) [113, 947, 56708] C5 x C45 42) [14177, 943, 218768] C5 x C45
11) [401, 362, 18325] C5 x C45 ---) [733, 181, 3609] C3 x C45
12) [401, 1379, 193808] C5 x C45 ---) [12113, 1763, 410624] C45
13) [401, 727, 35792] C5 x C45 ---) [2237, 617, 67769] C45
14) [401, 2779, 364304] C5 x C45 ---) [22769, 1843, 160400] C3 x C45
15) [401, 671, 83588] C5 x C45 ---) [20897, 1342, 115889] C45
16) [617, 990, 87073] C5 x C45 27) [1777, 495, 39488] C5 x C45
17) [701, 1081, 252709] C5 x C45 60) [252709, 2162, 157725] C5 x C45
18) [1093, 522, 63749] C5 x C45 ---) [1301, 261, 1093] C45
19) [1093, 237, 653] C5 x C45 ---) [653, 474, 53557] C45
20) [1093, 410, 2677] C5 x C45 ---) [2677, 205, 9837] C3 x C45
21) [1093, 1458, 317213] C5 x C45 ---) [1877, 729, 53557] C45
22) [1181, 1314, 426925] C5 x C45 46) [17077, 657, 1181] C5 x C45
23) [1217, 1223, 305476] C5 x C45 55) [76369, 2446, 273825] C5 x C45
24) [1409, 1207, 177872] C5 x C45 40) [11117, 2414, 745361] C5 x C45
25) [1429, 1042, 265725] C5 x C45 ---) [1181, 521, 1429] C45
26) [1429, 1510, 204201] C5 x C45 ---) [2521, 755, 91456] C45
27) [1777, 495, 39488] C5 x C45 16) [617, 990, 87073] C5 x C45
28) [2153, 527, 4304] C5 x C45 ---) [269, 809, 2153] C45
29) [2153, 835, 18752] C5 x C45 ---) [293, 505, 2153] C45
30) [2153, 1871, 784196] C5 x C45 ---) [4001, 2987, 861200] C3 x C45
31) [2389, 3858, 271325] C5 x C45 39) [10853, 1929, 862429] C5 x C45
32) [2473, 1083, 262928] C5 x C45 44) [16433, 2166, 121177] C5 x C45
33) [4357, 489, 32549] C5 x C45 ---) [269, 978, 108925] C45
34) [4441, 187, 7632] C5 x C45 ---) [53, 374, 4441] C45
35) [4441, 315, 23696] C5 x C45 ---) [1481, 630, 4441] C45
36) [6113, 314, 197] C5 x C45 ---) [197, 157, 6113] C45
37) [6481, 490, 34101] C5 x C45 ---) [421, 245, 6481] C45
38) [7817, 859, 26176] C5 x C45 ---) [409, 1718, 633177] C45
39) [10853, 1929, 862429] C5 x C45 31) [2389, 3858, 271325] C5 x C45
40) [11117, 2414, 745361] C5 x C45 24) [1409, 1207, 177872] C5 x C45
41) [12301, 113, 117] C5 x C45 ---) [13, 226, 12301] C45
42) [14177, 943, 218768] C5 x C45 10) [113, 947, 56708] C5 x C45
43) [15121, 1703, 418852] C5 x C45 ---) [2137, 3406, 1224801] C45
44) [16433, 2166, 121177] C5 x C45 32) [2473, 1083, 262928] C5 x C45
45) [16741, 737, 98125] C5 x C45 ---) [157, 1474, 150669] C45
46) [17077, 657, 1181] C5 x C45 22) [1181, 1314, 426925] C5 x C45
47) [23677, 329, 21141] C5 x C45 ---) [29, 658, 23677] C45
48) [23677, 1385, 97] C5 x C45 ---) [97, 1055, 94708] C45
49) [25153, 535, 65268] C5 x C45 ---) [37, 1045, 226377] C45
50) [30893, 185, 833] C5 x C45 ---) [17, 370, 30893] C45
51) [30949, 1549, 220725] C5 x C45 ---) [109, 1117, 278541] C45
52) [35509, 1338, 305525] C5 x C45 ---) [101, 669, 35509] C45
53) [38177, 199, 356] C5 x C45 ---) [89, 398, 38177] C45
54) [74597, 1346, 154541] C5 x C45 ---) [29, 673, 74597] C45
55) [76369, 2446, 273825] C5 x C45 23) [1217, 1223, 305476] C5 x C45
56) [92381, 633, 77077] C5 x C45 ---) [13, 957, 92381] C45
57) [106781, 409, 15125] C5 x C45 ---) [5, 677, 106781] C45
58) [195977, 1778, 6413] C5 x C45 7) [53, 889, 195977] C5 x C45
59) [199909, 2138, 343125] C5 x C45 8) [61, 1069, 199909] C5 x C45
60) [252709, 2162, 157725] C5 x C45 17) [701, 1081, 252709] C5 x C45
61) [258109, 1017, 194045] C5 x C45 ---) [5, 1081, 258109] C45
62) [270761, 563, 11552] C5 x C45 ---) [8, 1126, 270761] C45
63) [292601, 577, 10082] C5 x C45 ---) [8, 1154, 292601] C45
64) [294277, 1889, 229957] C5 x C45 ---) [13, 1085, 294277] C45
65) [305849, 587, 9680] C5 x C45 ---) [5, 1174, 305849] C45
66) [314189, 737, 57245] C5 x C45 ---) [5, 1141, 314189] C45
67) [354881, 607, 3392] C5 x C45 6) [53, 1214, 354881] C5 x C45
68) [403097, 635, 32] C5 x C45 ---) [8, 1270, 403097] C45
69) [406717, 697, 19773] C5 x C45 ---) [13, 1394, 406717] C45
70) [4589141, 3629, 2145125] C5 x C45 1) [5, 4337, 4589141] C5 x C45
71) [6441497, 2555, 21632] C5 x C45 3) [8, 5110, 6441497] C5 x C45