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 C105 non-normal (D4) quartic CM field invariants: 62 fields

K Quartic invariants Cl(OK) Igusa invariants Kr Reflex invariants Cl(OKr) Igusa invariants
1) [8, 3646, 3281857] C5 x C105 58) [3281857, 1823, 10368] C5 x C105
2) [8, 4750, 5615537] C5 x C105 ---) [5615537, 2375, 6272] C15 x C315
3) [8, 7990, 15558617] C5 x C105 62) [15558617, 3995, 100352] C5 x C105
4) [41, 2858, 1982837] C5 x C105 57) [1982837, 1429, 14801] C5 x C105
5) [337, 1695, 714128] C5 x C105 34) [44633, 3390, 16513] C5 x C105
6) [401, 2659, 1043264] C5 x C105 ---) [16301, 1405, 401] C105
7) [1429, 1817, 524925] C5 x C105 ---) [2333, 1329, 412981] C105
8) [1429, 1737, 93737] C5 x C105 ---) [1913, 967, 22864] C105
9) [1429, 285, 2801] C5 x C105 ---) [2801, 570, 70021] C105
10) [1777, 1967, 689616] C5 x C105 19) [4789, 3113, 783657] C5 x C105
11) [2081, 1554, 395629] C5 x C105 ---) [2341, 777, 52025] C105
12) [2081, 3127, 1295300] C5 x C105 ---) [12953, 4723, 133184] C105
13) [2081, 1067, 271616] C5 x C105 ---) [1061, 1049, 52025] C105
14) [2549, 541, 72533] C5 x C105 37) [72533, 1082, 2549] C5 x C105
15) [3121, 1311, 428900] C5 x C105 ---) [4289, 2622, 3121] C105
16) [3121, 639, 101300] C5 x C105 ---) [1013, 1278, 3121] C105
17) [3181, 341, 9189] C5 x C105 ---) [1021, 682, 79525] C105
18) [4357, 1682, 550429] C5 x C105 ---) [4549, 841, 39213] C105
19) [4789, 3113, 783657] C5 x C105 10) [1777, 1967, 689616] C5 x C105
20) [6113, 307, 9808] C5 x C105 ---) [613, 614, 55017] C105
21) [12041, 655, 80164] C5 x C105 ---) [409, 1310, 108369] C105
22) [12301, 4285, 2004021] C5 x C105 ---) [2749, 5621, 6507229] C105
23) [13229, 1022, 49457] C5 x C105 ---) [137, 511, 52916] C105
24) [13841, 1034, 211925] C5 x C105 ---) [173, 517, 13841] C105
25) [16001, 6230, 8679161] C5 x C105 ---) [3929, 3115, 256016] C105
26) [16001, 3262, 356017] C5 x C105 ---) [673, 1631, 576036] C105
27) [16741, 2218, 1162917] C5 x C105 ---) [293, 1109, 16741] C105
28) [18329, 155, 1424] C5 x C105 ---) [89, 310, 18329] C35
29) [18353, 2847, 2021764] C5 x C105 ---) [601, 2311, 660708] C105
30) [18773, 1325, 208937] C5 x C105 ---) [113, 1343, 300368] C105
31) [20389, 533, 65925] C5 x C105 ---) [293, 1066, 20389] C105
32) [32609, 738, 5725] C5 x C105 ---) [229, 369, 32609] C3 x C105
33) [36541, 2709, 290813] C5 x C105 ---) [173, 1433, 36541] C105
34) [44633, 3390, 16513] C5 x C105 5) [337, 1695, 714128] C5 x C105
35) [45989, 1186, 167693] C5 x C105 ---) [317, 593, 45989] C105
36) [48437, 978, 45373] C5 x C105 ---) [157, 489, 48437] C105
37) [72533, 1082, 2549] C5 x C105 14) [2549, 541, 72533] C5 x C105
38) [80749, 361, 12393] C5 x C105 ---) [17, 722, 80749] C105
39) [131893, 1802, 284229] C5 x C105 ---) [29, 901, 131893] C105
40) [164513, 559, 36992] C5 x C105 ---) [8, 1118, 164513] C105
41) [166301, 409, 245] C5 x C105 ---) [5, 818, 166301] C35
42) [181981, 1714, 6525] C5 x C105 ---) [29, 857, 181981] C105
43) [185477, 437, 1373] C5 x C105 ---) [1373, 874, 185477] C15 x C105
44) [187637, 437, 833] C5 x C105 ---) [17, 874, 187637] C105
45) [226217, 499, 5696] C5 x C105 ---) [89, 998, 226217] C105
46) [499801, 2159, 40768] C5 x C105 ---) [13, 1841, 499801] C105
47) [777097, 883, 648] C5 x C105 ---) [8, 1766, 777097] C105
48) [859561, 931, 1800] C5 x C105 ---) [8, 1862, 859561] C105
49) [924601, 1051, 45000] C5 x C105 ---) [8, 2102, 924601] C105
50) [972469, 1293, 174845] C5 x C105 ---) [5, 2009, 972469] C105
51) [987433, 1075, 42048] C5 x C105 ---) [73, 2150, 987433] C105
52) [1028569, 1019, 2448] C5 x C105 ---) [17, 2038, 1028569] C105
53) [1054301, 1609, 383645] C5 x C105 ---) [5, 2057, 1054301] C105
54) [1559017, 1747, 373248] C5 x C105 ---) [8, 3494, 1559017] C105
55) [1641737, 1283, 1088] C5 x C105 ---) [17, 2566, 1641737] C105
56) [1827949, 1393, 28125] C5 x C105 ---) [5, 2786, 1827949] C105
57) [1982837, 1429, 14801] C5 x C105 4) [41, 2858, 1982837] C5 x C105
58) [3281857, 1823, 10368] C5 x C105 1) [8, 3646, 3281857] C5 x C105
59) [3397469, 3193, 1699445] C5 x C105 ---) [5, 3749, 3397469] C105
60) [3738509, 2833, 1071845] C5 x C105 ---) [5, 3869, 3738509] C105
61) [3745589, 3197, 1618805] C5 x C105 ---) [5, 3901, 3745589] C105
62) [15558617, 3995, 100352] C5 x C105 3) [8, 7990, 15558617] C5 x C105