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 C85 non-normal (D4) quartic CM field invariants: 63 fields

K Quartic invariants Cl(OK) Igusa invariants Kr Reflex invariants Cl(OKr) Igusa invariants
1) [29, 3202, 2557517] C5 x C85 62) [2557517, 1601, 1421] C5 x C85
2) [73, 9494, 19842937] C5 x C85 63) [19842937, 4747, 672768] C5 x C85
3) [97, 2882, 2045053] C5 x C85 61) [2045053, 1441, 7857] C5 x C85
4) [401, 4927, 246212] C5 x C85 ---) [61553, 2563, 1257536] C85
5) [1093, 209, 8461] C5 x C85 ---) [8461, 418, 9837] C85
6) [1093, 1646, 519937] C5 x C85 ---) [4297, 823, 39348] C85
7) [1381, 381, 19373] C5 x C85 37) [19373, 762, 67669] C5 x C85
8) [2153, 390, 3577] C5 x C85 ---) [73, 195, 8612] C85
9) [2237, 4270, 1659073] C5 x C85 28) [9817, 2135, 724788] C5 x C85
10) [2749, 4902, 5963417] C5 x C85 ---) [11273, 2451, 10996] C5 x C5 x C85
11) [3041, 2855, 1635584] C5 x C85 24) [6389, 3481, 76025] C5 x C85
12) [3181, 1149, 195653] C5 x C85 ---) [677, 1021, 3181] C85
13) [3253, 470, 3177] C5 x C85 ---) [353, 235, 13012] C85
14) [3517, 481, 56961] C5 x C85 23) [6329, 962, 3517] C5 x C85
15) [4357, 1921, 738477] C5 x C85 ---) [1013, 1185, 4357] C85
16) [4441, 666, 93125] C5 x C85 ---) [149, 333, 4441] C85
17) [4441, 1699, 400788] C5 x C85 ---) [1237, 1621, 359721] C85
18) [4517, 2025, 888517] C5 x C85 35) [18133, 4050, 546557] C5 x C85
19) [4889, 1126, 4073] C5 x C85 ---) [4073, 563, 78224] C85
20) [4973, 4353, 1990813] C5 x C85 34) [16453, 8706, 10985357] C5 x C85
21) [5657, 4639, 2516224] C5 x C85 ---) [9829, 7753, 458217] C5 x C5 x C85
22) [6113, 394, 14357] C5 x C85 ---) [293, 197, 6113] C85
23) [6329, 962, 3517] C5 x C85 14) [3517, 481, 56961] C5 x C85
24) [6389, 3481, 76025] C5 x C85 11) [3041, 2855, 1635584] C5 x C85
25) [6949, 329, 11425] C5 x C85 ---) [457, 658, 62541] C85
26) [7229, 442, 19925] C5 x C85 ---) [797, 221, 7229] C85
27) [7817, 554, 45461] C5 x C85 ---) [269, 277, 7817] C85
28) [9817, 2135, 724788] C5 x C85 9) [2237, 4270, 1659073] C5 x C85
29) [9829, 1889, 5013] C5 x C85 ---) [557, 1569, 481621] C85
30) [11273, 3702, 2704729] C5 x C85 ---) [1609, 1851, 180368] C85
31) [12101, 2133, 263125] C5 x C85 ---) [421, 1197, 302525] C85
32) [12101, 1054, 84113] C5 x C85 ---) [233, 527, 48404] C85
33) [13841, 3239, 2342500] C5 x C85 ---) [937, 2739, 885824] C85
34) [16453, 8706, 10985357] C5 x C85 20) [4973, 4353, 1990813] C5 x C85
35) [18133, 4050, 546557] C5 x C85 18) [4517, 2025, 888517] C5 x C85
36) [18253, 4258, 955053] C5 x C85 ---) [877, 2129, 894397] C85
37) [19373, 762, 67669] C5 x C85 7) [1381, 381, 19373] C5 x C85
38) [27893, 1285, 71117] C5 x C85 ---) [197, 2570, 1366757] C85
39) [42437, 2482, 1370333] C5 x C85 ---) [173, 1241, 42437] C85
40) [44741, 421, 33125] C5 x C85 ---) [53, 842, 44741] C85
41) [80537, 443, 28928] C5 x C85 ---) [113, 886, 80537] C85
42) [100673, 335, 2888] C5 x C85 ---) [8, 670, 100673] C85
43) [109433, 1035, 240448] C5 x C85 ---) [13, 777, 109433] C85
44) [113453, 337, 29] C5 x C85 ---) [29, 674, 113453] C85
45) [147253, 1538, 2349] C5 x C85 ---) [29, 769, 147253] C85
46) [156353, 4158, 1820593] C5 x C85 ---) [97, 2079, 625412] C85
47) [176369, 863, 142100] C5 x C85 ---) [29, 1726, 176369] C85
48) [212081, 487, 6272] C5 x C85 ---) [8, 974, 212081] C85
49) [271261, 521, 45] C5 x C85 ---) [5, 1042, 271261] C85
50) [367021, 849, 88445] C5 x C85 ---) [5, 1217, 367021] C85
51) [373193, 611, 32] C5 x C85 ---) [8, 1222, 373193] C85
52) [471193, 699, 4352] C5 x C85 ---) [17, 1398, 471193] C85
53) [541529, 1243, 250880] C5 x C85 ---) [5, 1489, 541529] C85
54) [698713, 859, 9792] C5 x C85 ---) [17, 1718, 698713] C85
55) [891389, 953, 4205] C5 x C85 ---) [5, 1906, 891389] C85
56) [932149, 973, 3645] C5 x C85 ---) [5, 1946, 932149] C85
57) [946901, 1661, 453005] C5 x C85 ---) [5, 1973, 946901] C85
58) [1497149, 1513, 198005] C5 x C85 ---) [5, 2549, 1497149] C85
59) [1677997, 1297, 1053] C5 x C85 ---) [13, 2594, 1677997] C85
60) [1874549, 1373, 2645] C5 x C85 ---) [5, 2746, 1874549] C85
61) [2045053, 1441, 7857] C5 x C85 3) [97, 2882, 2045053] C5 x C85
62) [2557517, 1601, 1421] C5 x C85 1) [29, 3202, 2557517] C5 x C85
63) [19842937, 4747, 672768] C5 x C85 2) [73, 9494, 19842937] C5 x C85