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 C35 non-normal (D4) quartic CM field invariants: 65 fields

K Quartic invariants Cl(OK) Igusa invariants Kr Reflex invariants Cl(OKr) Igusa invariants
1) [5, 2833, 1714861] C5 x C35 60) [1714861, 1521, 149645] C5 x C35
2) [8, 4438, 4792889] C5 x C35 64) [4792889, 2219, 32768] C5 x C35
3) [8, 5078, 6434969] C5 x C35 65) [6434969, 2539, 2888] C5 x C35
4) [8, 3718, 3375881] C5 x C35 63) [3375881, 1859, 20000] C5 x C35
5) [8, 3254, 2567129] C5 x C35 62) [2567129, 1627, 20000] C5 x C35
6) [13, 3137, 1739209] C5 x C35 61) [1739209, 3959, 5200] C5 x C35
7) [29, 1669, 677533] C5 x C35 59) [677533, 3338, 75429] C5 x C35
8) [53, 1197, 302221] C5 x C35 57) [302221, 2394, 223925] C5 x C35
9) [157, 822, 45833] C5 x C35 49) [45833, 411, 30772] C5 x C35
10) [293, 1761, 28057] C5 x C35 44) [28057, 3051, 300032] C5 x C35
11) [401, 1907, 560192] C5 x C35 ---) [8753, 1511, 463556] C35
12) [401, 675, 101776] C5 x C35 ---) [6361, 1350, 48521] C35
13) [1013, 258, 12589] C5 x C35 ---) [12589, 129, 1013] C5 x C385
14) [1033, 2158, 751041] C5 x C35 52) [83449, 1079, 103300] C5 x C35
15) [1093, 133, 4149] C5 x C35 ---) [461, 266, 1093] C35
16) [1109, 4582, 3101657] C5 x C35 ---) [18353, 2291, 536756] C5 x C5 x C35
17) [1429, 458, 997] C5 x C35 ---) [997, 229, 12861] C35
18) [1429, 281, 16525] C5 x C35 ---) [661, 562, 12861] C35
19) [1453, 402, 34589] C5 x C35 45) [34589, 201, 1453] C5 x C35
20) [2081, 902, 70217] C5 x C35 ---) [1433, 451, 33296] C35
21) [2081, 2323, 1344400] C5 x C35 ---) [3361, 2571, 1631504] C35
22) [2153, 115, 2768] C5 x C35 ---) [173, 230, 2153] C35
23) [2477, 177, 7213] C5 x C35 35) [7213, 354, 2477] C5 x C35
24) [3121, 670, 62289] C5 x C35 ---) [769, 335, 12484] C35
25) [3181, 1213, 80757] C5 x C35 ---) [997, 1541, 537589] C35
26) [3457, 347, 22324] C5 x C35 33) [5581, 694, 31113] C5 x C35
27) [4073, 6166, 2988089] C5 x C35 43) [17681, 3083, 1629200] C5 x C35
28) [4441, 815, 31716] C5 x C35 ---) [881, 1630, 537361] C35
29) [4561, 1763, 274192] C5 x C35 42) [17137, 3526, 2011401] C5 x C35
30) [4889, 2395, 102976] C5 x C35 ---) [1609, 1915, 704016] C35
31) [5449, 4427, 2827600] C5 x C35 34) [7069, 4385, 2882521] C5 x C35
32) [5569, 4991, 1704100] C5 x C35 41) [17041, 9982, 18093681] C5 x C35
33) [5581, 694, 31113] C5 x C35 26) [3457, 347, 22324] C5 x C35
34) [7069, 4385, 2882521] C5 x C35 31) [5449, 4427, 2827600] C5 x C35
35) [7213, 354, 2477] C5 x C35 23) [2477, 177, 7213] C5 x C35
36) [7229, 89, 173] C5 x C35 ---) [173, 178, 7229] C35
37) [10909, 594, 44573] C5 x C35 ---) [53, 297, 10909] C35
38) [11273, 1214, 188081] C5 x C35 ---) [521, 607, 45092] C35
39) [11273, 503, 37888] C5 x C35 ---) [37, 417, 11273] C35
40) [16741, 925, 8829] C5 x C35 ---) [109, 1433, 16741] C35
41) [17041, 9982, 18093681] C5 x C35 32) [5569, 4991, 1704100] C5 x C35
42) [17137, 3526, 2011401] C5 x C35 29) [4561, 1763, 274192] C5 x C35
43) [17681, 3083, 1629200] C5 x C35 27) [4073, 6166, 2988089] C5 x C35
44) [28057, 3051, 300032] C5 x C35 10) [293, 1761, 28057] C5 x C35
45) [34589, 201, 1453] C5 x C35 19) [1453, 402, 34589] C5 x C35
46) [35593, 643, 94464] C5 x C35 ---) [41, 1286, 35593] C35
47) [41777, 1187, 91136] C5 x C35 ---) [89, 1643, 668432] C35
48) [43037, 866, 15341] C5 x C35 ---) [29, 433, 43037] C35
49) [45833, 411, 30772] C5 x C35 9) [157, 822, 45833] C5 x C35
50) [48437, 665, 1573] C5 x C35 ---) [13, 549, 48437] C35
51) [57853, 869, 58621] C5 x C35 ---) [61, 1738, 520677] C35
52) [83449, 1079, 103300] C5 x C35 14) [1033, 2158, 751041] C5 x C35
53) [112601, 337, 242] C5 x C35 ---) [8, 674, 112601] C35
54) [115337, 547, 45968] C5 x C35 ---) [17, 1094, 115337] C35
55) [120829, 393, 8405] C5 x C35 ---) [5, 769, 120829] C35
56) [200029, 457, 2205] C5 x C35 ---) [5, 914, 200029] C35
57) [302221, 2394, 223925] C5 x C35 8) [53, 1197, 302221] C5 x C35
58) [338669, 1217, 285605] C5 x C35 ---) [5, 1261, 338669] C35
59) [677533, 3338, 75429] C5 x C35 7) [29, 1669, 677533] C5 x C35
60) [1714861, 1521, 149645] C5 x C35 1) [5, 2833, 1714861] C5 x C35
61) [1739209, 3959, 5200] C5 x C35 6) [13, 3137, 1739209] C5 x C35
62) [2567129, 1627, 20000] C5 x C35 5) [8, 3254, 2567129] C5 x C35
63) [3375881, 1859, 20000] C5 x C35 4) [8, 3718, 3375881] C5 x C35
64) [4792889, 2219, 32768] C5 x C35 2) [8, 4438, 4792889] C5 x C35
65) [6434969, 2539, 2888] C5 x C35 3) [8, 5078, 6434969] C5 x C35