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 C18 x C36 non-normal (D4) quartic CM field invariants: 102 fields

K Quartic invariants Cl(OK) Igusa invariants Kr Reflex invariants Cl(OKr) Igusa invariants
1) [5, 6558, 10103841] C18 x C36 101) [1122649, 3279, 162000] C18 x C36
2) [21, 1934, 930973] C18 x C36 99) [930973, 967, 1029] C18 x C36
3) [29, 4318, 4594465] C18 x C36 ---) [4594465, 2159, 16704] C18 x C792
4) [33, 1646, 668881] C18 x C36 ---) [668881, 823, 2112] C2 x C18 x C36
5) [40, 1292, 399676] C18 x C36 95) [399676, 646, 4410] C18 x C36
6) [60, 1074, 287409] C18 x C36 ---) [287409, 537, 240] C18 x C18
7) [60, 418, 38821] C18 x C36 ---) [38821, 209, 1215] C18 x C18
8) [76, 2486, 1323433] C18 x C36 ---) [1323433, 1243, 55404] C18 x C72
9) [77, 706, 118372] C18 x C36 ---) [29593, 1412, 24948] C2 x C18 x C36
10) [85, 2774, 1727929] C18 x C36 ---) [1727929, 1387, 48960] C18 x C72
11) [92, 8038, 13797161] C18 x C36 ---) [13797161, 4019, 588800] C9 x C72
12) [92, 6502, 10563113] C18 x C36 ---) [10563113, 3251, 1472] C2 x C18 x C36
13) [101, 2406, 734553] C18 x C36 ---) [81617, 1203, 178164] C18 x C360
14) [177, 6950, 10444393] C18 x C36 ---) [10444393, 3475, 407808] C2 x C18 x C252
15) [236, 1886, 511649] C18 x C36 ---) [511649, 943, 94400] C18 x C72
16) [253, 2537, 1130353] C18 x C36 ---) [1130353, 5074, 1914957] C36 x C144
17) [264, 3482, 2891425] C18 x C36 ---) [115657, 1741, 34914] C18 x C18
18) [280, 6022, 8779401] C18 x C36 ---) [975489, 3011, 71680] C3 x C18 x C18
19) [421, 2057, 784057] C18 x C36 ---) [2713, 4114, 1095021] C3 x C9 x C72
20) [440, 414, 11059] C18 x C36 ---) [44236, 828, 127160] C18 x C18
21) [456, 1164, 278418] C18 x C36 68) [22728, 1116, 32946] C18 x C36
22) [460, 806, 125149] C18 x C36 ---) [125149, 403, 9315] C18 x C234
23) [461, 442, 41465] C18 x C36 ---) [41465, 221, 1844] C6 x C18 x C36
24) [476, 1046, 151673] C18 x C36 ---) [151673, 523, 30464] C18 x C18
25) [501, 1829, 808129] C18 x C36 ---) [808129, 3658, 112725] C18 x C72
26) [616, 1810, 641001] C18 x C36 ---) [641001, 905, 44506] C18 x C144
27) [677, 1521, 576837] C18 x C36 82) [64093, 3042, 6093] C18 x C36
28) [716, 3350, 2072441] C18 x C36 ---) [2072441, 1675, 183296] C18 x C360
29) [737, 6390, 3415833] C18 x C36 ---) [379537, 3195, 1698048] C6 x C18 x C72
30) [748, 528, 33044] C18 x C36 ---) [8261, 264, 9163] C18 x C18
31) [1036, 318, 8705] C18 x C36 ---) [8705, 159, 4144] C18 x C72
32) [1057, 1222, 166149] C18 x C36 64) [18461, 611, 51793] C18 x C36
33) [1129, 247, 1422] C18 x C36 ---) [632, 494, 55321] C2 x C36
34) [1129, 512, 24892] C18 x C36 ---) [508, 256, 10161] C2 x C36
35) [1129, 605, 43806] C18 x C36 ---) [3576, 1210, 190801] C6 x C72
36) [1129, 979, 158040] C18 x C36 ---) [17560, 1958, 326281] C4 x C36
37) [1129, 204, 9275] C18 x C36 ---) [1484, 408, 4516] C2 x C72
38) [1129, 2290, 5901] C18 x C36 ---) [5901, 1145, 326281] C6 x C72
39) [1129, 1171, 342528] C18 x C36 ---) [5352, 2342, 1129] C2 x C72
40) [1129, 1189, 82188] C18 x C36 ---) [9132, 2378, 1084969] C2 x C72
41) [1144, 660, 74294] C18 x C36 ---) [2456, 780, 48334] C18 x C18
42) [1253, 1145, 319925] C18 x C36 ---) [12797, 2290, 31325] C2 x C18 x C18
43) [1529, 239, 13898] C18 x C36 ---) [55592, 478, 1529] C36 x C36
44) [1532, 632, 98324] C18 x C36 ---) [24581, 316, 383] C9 x C72
45) [1852, 390, 30617] C18 x C36 ---) [30617, 195, 1852] C2 x C18 x C36
46) [2012, 2744, 1334617] C18 x C36 50) [3697, 1670, 72432] C18 x C36
47) [2065, 1077, 62316] C18 x C36 ---) [6924, 2154, 910665] C18 x C72
48) [2121, 386, 28765] C18 x C36 71) [28765, 193, 2121] C18 x C36
49) [3301, 4237, 3100797] C18 x C36 ---) [344533, 8474, 5548981] C3 x C18 x C72
50) [3697, 1670, 72432] C18 x C36 46) [2012, 2744, 1334617] C18 x C36
51) [5521, 158, 720] C18 x C36 ---) [5, 316, 22084] C72
52) [6376, 1286, 101025] C18 x C36 ---) [449, 643, 78106] C18 x C18
53) [6568, 352, 24408] C18 x C36 ---) [2712, 176, 1642] C2 x C18 x C18
54) [6616, 202, 3585] C18 x C36 ---) [3585, 101, 1654] C2 x C360
55) [7144, 90, 239] C18 x C36 ---) [956, 180, 7144] C18 x C18
56) [7465, 487, 12636] C18 x C36 ---) [156, 974, 186625] C2 x C36
57) [8009, 1633, 424400] C18 x C36 ---) [1061, 2663, 200225] C9 x C72
58) [9532, 4982, 4594173] C18 x C36 ---) [2733, 2491, 402727] C9 x C72
59) [10433, 1129, 316052] C18 x C36 ---) [653, 2258, 10433] C9 x C72
60) [11641, 434, 525] C18 x C36 ---) [21, 217, 11641] C72
61) [12409, 1127, 66250] C18 x C36 ---) [424, 2254, 1005129] C2 x C72
62) [12409, 1297, 417450] C18 x C36 ---) [552, 2594, 12409] C2 x C2 x C36
63) [12657, 255, 13092] C18 x C36 ---) [3273, 510, 12657] C72
64) [18461, 611, 51793] C18 x C36 32) [1057, 1222, 166149] C18 x C36
65) [18633, 177, 3174] C18 x C36 ---) [24, 354, 18633] C72
66) [20545, 436, 26979] C18 x C36 ---) [204, 872, 82180] C2 x C36
67) [21865, 687, 68796] C18 x C36 ---) [156, 1374, 196785] C2 x C36
68) [22728, 1116, 32946] C18 x C36 21) [456, 1164, 278418] C18 x C36
69) [24169, 346, 5760] C18 x C36 ---) [40, 692, 96676] C2 x C72
70) [28732, 172, 213] C18 x C36 ---) [213, 344, 28732] C18 x C18
71) [28765, 193, 2121] C18 x C36 48) [2121, 386, 28765] C18 x C36
72) [30181, 177, 287] C18 x C36 ---) [1148, 354, 30181] C2 x C18 x C36
73) [31564, 718, 2625] C18 x C36 ---) [105, 359, 31564] C2 x C36
74) [31897, 985, 43200] C18 x C36 ---) [12, 1970, 797425] C2 x C2 x C18
75) [39196, 736, 96228] C18 x C36 ---) [33, 368, 9799] C2 x C18
76) [39992, 802, 833] C18 x C36 ---) [17, 401, 39992] C2 x C36
77) [43256, 836, 1700] C18 x C36 ---) [17, 418, 43256] C2 x C36
78) [48904, 1092, 102500] C18 x C36 ---) [41, 546, 48904] C36
79) [49785, 476, 6859] C18 x C36 ---) [76, 952, 199140] C2 x C18
80) [59781, 1050, 36501] C18 x C36 ---) [69, 525, 59781] C72
81) [60193, 247, 204] C18 x C36 ---) [204, 494, 60193] C4 x C36
82) [64093, 3042, 6093] C18 x C36 27) [677, 1521, 576837] C18 x C36
83) [71161, 385, 19266] C18 x C36 ---) [456, 770, 71161] C2 x C72
84) [71497, 379, 18036] C18 x C36 ---) [501, 758, 71497] C18 x C18
85) [75497, 467, 35648] C18 x C36 ---) [557, 934, 75497] C9 x C36
86) [102841, 811, 138720] C18 x C36 ---) [120, 1622, 102841] C4 x C36
87) [117217, 1971, 707472] C18 x C36 ---) [17, 3942, 1054953] C2 x C36
88) [136105, 766, 10584] C18 x C36 ---) [24, 1532, 544420] C2 x C18
89) [149849, 987, 206080] C18 x C36 ---) [805, 1974, 149849] C18 x C72
90) [197724, 890, 301] C18 x C36 ---) [301, 445, 49431] C18 x C18
91) [295916, 544, 5] C18 x C36 ---) [5, 1088, 295916] C18 x C18
92) [303544, 1180, 272214] C18 x C36 ---) [24, 788, 75886] C18 x C18
93) [328417, 625, 15552] C18 x C36 ---) [12, 1250, 328417] C2 x C18
94) [341849, 779, 66248] C18 x C36 ---) [8, 1558, 341849] C2 x C18
95) [399676, 646, 4410] C18 x C36 5) [40, 1292, 399676] C18 x C36
96) [431385, 659, 724] C18 x C36 ---) [181, 1318, 431385] C18 x C18
97) [787373, 919, 14297] C18 x C36 ---) [17, 1838, 787373] C2 x C18 x C18
98) [829489, 967, 26400] C18 x C36 ---) [264, 1934, 829489] C2 x C2 x C18 x C18
99) [930973, 967, 1029] C18 x C36 2) [21, 1934, 930973] C18 x C36
100) [993081, 1067, 36352] C18 x C36 ---) [568, 2134, 993081] C3 x C9 x C72
101) [1122649, 3279, 162000] C18 x C36 1) [5, 6558, 10103841] C18 x C36
102) [3419841, 3071, 1502800] C18 x C36 ---) [13, 6142, 3419841] C18 x C18