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 C3 x C6 x C36 non-normal (D4) quartic CM field invariants: 88 fields

K Quartic invariants Cl(OK) Igusa invariants Kr Reflex invariants Cl(OKr) Igusa invariants
1) [201, 5846, 7501945] C3 x C6 x C36 ---) [7501945, 2923, 260496] C3 x C12 x C72
2) [229, 1430, 379321] C3 x C6 x C36 ---) [379321, 715, 32976] C12 x C72
3) [229, 524, 2463] C3 x C6 x C36 ---) [9852, 1048, 264724] C6 x C72
4) [257, 466, 53261] C3 x C6 x C36 ---) [53261, 233, 257] C12 x C72
5) [257, 775, 150092] C3 x C6 x C36 ---) [150092, 1550, 257] C6 x C72
6) [316, 2134, 1012089] C3 x C6 x C36 ---) [1012089, 1067, 31600] C12 x C72
7) [316, 816, 52388] C3 x C6 x C36 ---) [13097, 408, 28519] C3 x C72
8) [316, 234, 13373] C3 x C6 x C36 ---) [13373, 117, 79] C3 x C72
9) [316, 534, 51065] C3 x C6 x C36 ---) [51065, 267, 5056] C6 x C72
10) [316, 478, 41637] C3 x C6 x C36 ---) [41637, 239, 3871] C3 x C72
11) [321, 1011, 157224] C3 x C6 x C36 ---) [157224, 2022, 393225] C6 x C72
12) [469, 379, 35793] C3 x C6 x C36 ---) [3977, 758, 469] C2 x C6 x C36
13) [568, 1102, 234873] C3 x C6 x C36 ---) [26097, 551, 17182] C6 x C36
14) [568, 578, 42483] C3 x C6 x C36 ---) [12, 442, 41038] C2 x C6 x C18
15) [568, 484, 56292] C3 x C6 x C36 ---) [14073, 242, 568] C6 x C36
16) [761, 566, 3989] C3 x C6 x C36 ---) [3989, 283, 19025] C3 x C72
17) [892, 190, 8133] C3 x C6 x C36 ---) [8133, 95, 223] C3 x C72
18) [940, 2014, 51489] C3 x C6 x C36 ---) [5721, 1007, 240640] C6 x C18
19) [940, 454, 36489] C3 x C6 x C36 ---) [36489, 227, 3760] C3 x C6 x C18
20) [993, 926, 198481] C3 x C6 x C36 ---) [198481, 463, 3972] C12 x C36
21) [1384, 230, 769] C3 x C6 x C36 ---) [769, 115, 3114] C6 x C18
22) [1384, 1892, 446500] C3 x C6 x C36 ---) [4465, 946, 112104] C6 x C36
23) [1384, 178, 7575] C3 x C6 x C36 ---) [1212, 356, 1384] C6 x C36
24) [1436, 434, 29498] C3 x C6 x C36 ---) [2408, 868, 70364] C6 x C72
25) [1489, 1995, 991656] C3 x C6 x C36 ---) [110184, 3990, 13401] C6 x C72
26) [1833, 1664, 382447] C3 x C6 x C36 ---) [9052, 3328, 1239108] C3 x C3 x C6 x C36
27) [1929, 345, 25416] C3 x C6 x C36 ---) [2824, 690, 17361] C12 x C72
28) [2296, 866, 1513] C3 x C6 x C36 ---) [1513, 433, 46494] C6 x C36
29) [2713, 191, 3016] C3 x C6 x C36 ---) [3016, 382, 24417] C2 x C6 x C72
30) [2857, 1291, 381672] C3 x C6 x C36 ---) [4712, 2582, 139993] C6 x C72
31) [3580, 630, 9725] C3 x C6 x C36 ---) [389, 315, 22375] C6 x C18
32) [3580, 434, 32769] C3 x C6 x C36 ---) [3641, 217, 3580] C6 x C18
33) [3592, 80, 702] C3 x C6 x C36 ---) [312, 160, 3592] C6 x C36
34) [4237, 2089, 1039077] C3 x C6 x C36 ---) [115453, 4178, 207613] C3 x C6 x C72
35) [5261, 1517, 353045] C3 x C6 x C36 ---) [7205, 3034, 889109] C12 x C72
36) [5624, 806, 72425] C3 x C6 x C36 ---) [2897, 403, 22496] C6 x C18
37) [5853, 322, 2509] C3 x C6 x C36 ---) [2509, 161, 5853] C2 x C6 x C36
38) [7053, 153, 4089] C3 x C6 x C36 ---) [4089, 306, 7053] C6 x C72
39) [7948, 1378, 466773] C3 x C6 x C36 ---) [1293, 689, 1987] C3 x C72
40) [8396, 692, 111320] C3 x C6 x C36 ---) [920, 346, 2099] C12 x C36
41) [9836, 1852, 60760] C3 x C6 x C36 ---) [1240, 926, 199179] C6 x C72
42) [11965, 274, 6804] C3 x C6 x C36 ---) [21, 548, 47860] C6 x C18
43) [14680, 598, 85731] C3 x C6 x C36 ---) [204, 626, 3670] C6 x C36
44) [15709, 550, 12789] C3 x C6 x C36 ---) [29, 275, 15709] C6 x C36
45) [16201, 355, 27456] C3 x C6 x C36 ---) [429, 710, 16201] C2 x C6 x C18
46) [17929, 608, 20700] C3 x C6 x C36 ---) [92, 304, 17929] C6 x C36
47) [18853, 283, 15309] C3 x C6 x C36 ---) [21, 566, 18853] C6 x C18
48) [20093, 143, 89] C3 x C6 x C36 ---) [89, 286, 20093] C2 x C6 x C18
49) [20649, 149, 388] C3 x C6 x C36 ---) [97, 298, 20649] C2 x C6 x C18
50) [26933, 187, 2009] C3 x C6 x C36 ---) [41, 374, 26933] C2 x C6 x C18
51) [27708, 446, 22021] C3 x C6 x C36 ---) [61, 223, 6927] C6 x C18
52) [28165, 181, 1149] C3 x C6 x C36 ---) [1149, 362, 28165] C6 x C18
53) [29273, 525, 3042] C3 x C6 x C36 ---) [8, 1050, 263457] C6 x C18
54) [29485, 706, 6669] C3 x C6 x C36 ---) [741, 353, 29485] C6 x C36
55) [29901, 401, 32725] C3 x C6 x C36 ---) [1309, 802, 29901] C6 x C72
56) [44033, 1115, 35600] C3 x C6 x C36 ---) [89, 2230, 1100825] C2 x C6 x C18
57) [48469, 363, 20825] C3 x C6 x C36 ---) [17, 726, 48469] C2 x C6 x C18
58) [52645, 475, 43245] C3 x C6 x C36 ---) [5, 495, 52645] C6 x C18
59) [55628, 1084, 238136] C3 x C6 x C36 ---) [824, 542, 13907] C3 x C3 x C72
60) [56777, 1008, 26908] C3 x C6 x C36 ---) [28, 504, 56777] C2 x C6 x C18
61) [62041, 859, 168960] C3 x C6 x C36 ---) [165, 1718, 62041] C12 x C36
62) [70921, 1867, 2640] C3 x C6 x C36 ---) [165, 3485, 1773025] C6 x C72
63) [80121, 620, 15979] C3 x C6 x C36 ---) [76, 1240, 320484] C6 x C18
64) [88817, 377, 13328] C3 x C6 x C36 ---) [17, 754, 88817] C6 x C36
65) [102057, 714, 25392] C3 x C6 x C36 ---) [12, 876, 102057] C6 x C36
66) [105505, 1035, 30420] C3 x C6 x C36 ---) [5, 2070, 949545] C6 x C18
67) [106909, 517, 40095] C3 x C6 x C36 ---) [220, 1034, 106909] C2 x C6 x C36
68) [116396, 728, 16100] C3 x C6 x C36 ---) [161, 364, 29099] C6 x C18
69) [139849, 1258, 255792] C3 x C6 x C36 ---) [12, 764, 139849] C6 x C36
70) [164953, 2947, 150528] C3 x C6 x C36 ---) [12, 5894, 8082697] C6 x C36
71) [191804, 1758, 5425] C3 x C6 x C36 ---) [217, 879, 191804] C3 x C72
72) [219001, 1503, 72000] C3 x C6 x C36 ---) [5, 3006, 1971009] C3 x C72
73) [264913, 1150, 65712] C3 x C6 x C36 ---) [12, 1412, 264913] C6 x C36
74) [376457, 1091, 203456] C3 x C6 x C36 ---) [44, 2182, 376457] C6 x C18
75) [438505, 1651, 571824] C3 x C6 x C36 ---) [44, 3302, 438505] C3 x C36
76) [449637, 725, 18997] C3 x C6 x C36 ---) [157, 1450, 449637] C3 x C6 x C18
77) [474649, 2299, 1202688] C3 x C6 x C36 ---) [232, 4598, 474649] C2 x C6 x C36
78) [535569, 2235, 43776] C3 x C6 x C36 ---) [76, 4470, 4820121] C6 x C18
79) [599441, 2811, 626688] C3 x C6 x C36 ---) [17, 5622, 5394969] C6 x C36
80) [628905, 1011, 98304] C3 x C6 x C36 ---) [24, 2022, 628905] C6 x C18
81) [632705, 3995, 35600] C3 x C6 x C36 ---) [89, 7403, 10123280] C3 x C36
82) [798465, 1794, 6144] C3 x C6 x C36 ---) [24, 3588, 3193860] C6 x C18
83) [941569, 1087, 60000] C3 x C6 x C36 ---) [24, 2174, 941569] C3 x C72
84) [1325113, 1579, 292032] C3 x C6 x C36 ---) [12, 3158, 1325113] C3 x C36
85) [1441169, 1207, 3920] C3 x C6 x C36 ---) [5, 2414, 1441169] C6 x C18
86) [1527401, 1555, 222656] C3 x C6 x C36 ---) [284, 3110, 1527401] C3 x C6 x C18
87) [1668217, 1387, 63888] C3 x C6 x C36 ---) [33, 2774, 1668217] C6 x C18
88) [1699513, 1409, 71442] C3 x C6 x C36 ---) [8, 2818, 1699513] C6 x C18