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 C213 non-normal (D4) quartic CM field invariants: 104 fields

K Quartic invariants Cl(OK) Igusa invariants Kr Reflex invariants Cl(OKr) Igusa invariants
1) [13, 6150, 6846473] C3 x C213 99) [6846473, 3075, 652288] C3 x C213
2) [13, 7149, 12569021] C3 x C213 103) [12569021, 13333, 16161925] C3 x C213
3) [73, 7494, 9255881] C3 x C213 102) [9255881, 3747, 1196032] C3 x C213
4) [73, 918, 153449] C3 x C213 ---) [153449, 459, 14308] C3 x C2343
5) [73, 6438, 9165929] C3 x C213 101) [9165929, 3219, 299008] C3 x C213
6) [97, 1314, 412637] C3 x C213 81) [412637, 657, 4753] C3 x C213
7) [113, 726, 43177] C3 x C213 67) [43177, 363, 22148] C3 x C213
8) [113, 5462, 7393273] C3 x C213 ---) [7393273, 2731, 16272] C3 x C1491
9) [229, 277, 6301] C3 x C213 ---) [6301, 554, 51525] C213
10) [229, 2414, 269713] C3 x C213 ---) [269713, 1207, 296784] C213
11) [233, 755, 139652] C3 x C213 64) [34913, 1510, 11417] C3 x C213
12) [241, 1218, 369917] C3 x C213 80) [369917, 609, 241] C3 x C213
13) [257, 1606, 233609] C3 x C213 ---) [233609, 803, 102800] C213
14) [733, 613, 89361] C3 x C213 ---) [9929, 1226, 18325] C213
15) [733, 645, 37853] C3 x C213 ---) [37853, 1290, 264613] C213
16) [761, 2063, 569152] C3 x C213 ---) [8893, 2409, 274721] C213
17) [761, 283, 4612] C3 x C213 ---) [1153, 566, 61641] C213
18) [761, 1094, 104393] C3 x C213 ---) [104393, 547, 48704] C213
19) [773, 1490, 551933] C3 x C213 84) [551933, 745, 773] C3 x C213
20) [1153, 466, 12781] C3 x C213 50) [12781, 233, 10377] C3 x C213
21) [1489, 2314, 1332693] C3 x C213 ---) [16453, 1157, 1489] C213
22) [2213, 362, 23909] C3 x C213 61) [23909, 181, 2213] C3 x C213
23) [2213, 1477, 13709] C3 x C213 ---) [13709, 2954, 2126693] C213
24) [2777, 250, 4517] C3 x C213 ---) [4517, 125, 2777] C213
25) [2801, 2767, 1711700] C3 x C213 57) [17117, 5534, 809489] C3 x C213
26) [3697, 6546, 1470029] C3 x C213 48) [12149, 3273, 2310625] C3 x C213
27) [4001, 3947, 3053492] C3 x C213 ---) [4517, 2929, 2116529] C213
28) [4013, 670, 48017] C3 x C213 70) [48017, 335, 16052] C3 x C213
29) [4093, 4729, 137961] C3 x C213 54) [15329, 7591, 10232500] C3 x C213
30) [4493, 306, 5437] C3 x C213 ---) [5437, 153, 4493] C213
31) [4649, 306, 4813] C3 x C213 ---) [4813, 153, 4649] C213
32) [4793, 370, 15053] C3 x C213 53) [15053, 185, 4793] C3 x C213
33) [5081, 1042, 88525] C3 x C213 ---) [3541, 521, 45729] C213
34) [5189, 1253, 287425] C3 x C213 46) [11497, 2506, 420309] C3 x C213
35) [5297, 395, 27088] C3 x C213 ---) [1693, 790, 47673] C213
36) [5297, 1179, 123712] C3 x C213 ---) [1933, 2358, 895193] C213
37) [5297, 1458, 1741] C3 x C213 ---) [1741, 729, 132425] C213
38) [5333, 809, 2297] C3 x C213 ---) [2297, 1618, 645293] C213
39) [5741, 1522, 5021] C3 x C213 ---) [5021, 761, 143525] C213
40) [6133, 1445, 446877] C3 x C213 ---) [613, 1301, 55197] C213
41) [7673, 3103, 57296] C3 x C213 ---) [3581, 5437, 4059017] C213
42) [10301, 3034, 282293] C3 x C213 ---) [2333, 1517, 504749] C213
43) [10457, 559, 54592] C3 x C213 ---) [853, 1118, 94113] C213
44) [10457, 1947, 819604] C3 x C213 ---) [709, 2677, 847017] C213
45) [10733, 3962, 3881429] C3 x C213 ---) [2309, 1981, 10733] C213
46) [11497, 2506, 420309] C3 x C213 34) [5189, 1253, 287425] C3 x C213
47) [11789, 2986, 1050149] C3 x C213 ---) [2909, 1493, 294725] C213
48) [12149, 3273, 2310625] C3 x C213 26) [3697, 6546, 1470029] C3 x C213
49) [12577, 2166, 367961] C3 x C213 ---) [3041, 1083, 201232] C213
50) [12781, 233, 10377] C3 x C213 20) [1153, 466, 12781] C3 x C213
51) [13537, 4523, 5029776] C3 x C213 ---) [3881, 6507, 5414800] C213
52) [13877, 157, 2693] C3 x C213 ---) [2693, 314, 13877] C213
53) [15053, 185, 4793] C3 x C213 32) [4793, 370, 15053] C3 x C213
54) [15329, 7591, 10232500] C3 x C213 29) [4093, 4729, 137961] C3 x C213
55) [15733, 2445, 357797] C3 x C213 ---) [2957, 4890, 4546837] C213
56) [16661, 2586, 5749] C3 x C213 ---) [5749, 1293, 416525] C213
57) [17117, 5534, 809489] C3 x C213 25) [2801, 2767, 1711700] C3 x C213
58) [17477, 1090, 227117] C3 x C213 ---) [1877, 545, 17477] C213
59) [18269, 2706, 3709] C3 x C213 ---) [3709, 1353, 456725] C213
60) [20749, 837, 45461] C3 x C213 ---) [269, 1674, 518725] C213
61) [23909, 181, 2213] C3 x C213 22) [2213, 362, 23909] C3 x C213
62) [27437, 725, 69673] C3 x C213 ---) [193, 1450, 246933] C213
63) [32413, 2982, 148649] C3 x C213 ---) [281, 1491, 518608] C213
64) [34913, 1510, 11417] C3 x C213 11) [233, 755, 139652] C3 x C213
65) [35317, 786, 13181] C3 x C213 ---) [269, 393, 35317] C213
66) [39157, 2253, 789329] C3 x C213 ---) [281, 2443, 626512] C213
67) [43177, 363, 22148] C3 x C213 7) [113, 726, 43177] C3 x C213
68) [45641, 1939, 15700] C3 x C213 ---) [157, 2737, 410769] C213
69) [46589, 433, 35225] C3 x C213 ---) [1409, 866, 46589] C213
70) [48017, 335, 16052] C3 x C213 28) [4013, 670, 48017] C3 x C213
71) [66221, 2062, 3425] C3 x C213 ---) [137, 1031, 264884] C213
72) [81373, 641, 82377] C3 x C213 ---) [113, 1282, 81373] C213
73) [98573, 1402, 97109] C3 x C213 ---) [269, 701, 98573] C213
74) [110729, 379, 8228] C3 x C213 ---) [17, 758, 110729] C213
75) [137957, 373, 293] C3 x C213 ---) [293, 746, 137957] C213
76) [215417, 907, 151808] C3 x C213 ---) [593, 1814, 215417] C213
77) [235537, 5347, 22608] C3 x C213 ---) [157, 4177, 2119833] C213
78) [302213, 557, 2009] C3 x C213 ---) [41, 1114, 302213] C213
79) [359477, 669, 22021] C3 x C213 ---) [61, 1338, 359477] C213
80) [369917, 609, 241] C3 x C213 12) [241, 1218, 369917] C3 x C213
81) [412637, 657, 4753] C3 x C213 6) [97, 1314, 412637] C3 x C213
82) [431857, 703, 15588] C3 x C213 ---) [433, 1406, 431857] C213
83) [516689, 783, 24100] C3 x C213 ---) [241, 1566, 516689] C213
84) [551933, 745, 773] C3 x C213 19) [773, 1490, 551933] C3 x C213
85) [678641, 4163, 91136] C3 x C213 ---) [89, 8326, 16966025] C213
86) [926657, 3451, 892372] C3 x C213 ---) [13, 3441, 926657] C213
87) [944369, 1063, 46400] C3 x C213 ---) [29, 2126, 944369] C213
88) [997121, 1151, 81920] C3 x C213 ---) [5, 2173, 997121] C213
89) [1205653, 1213, 66429] C3 x C213 ---) [61, 2426, 1205653] C213
90) [1303129, 2107, 784080] C3 x C213 ---) [5, 2361, 1303129] C213
91) [1578749, 1257, 325] C3 x C213 ---) [13, 2514, 1578749] C213
92) [2407337, 1907, 307328] C3 x C213 ---) [8, 3814, 2407337] C213
93) [3077849, 1787, 28880] C3 x C213 ---) [5, 3574, 3077849] C213
94) [3303337, 1843, 23328] C3 x C213 ---) [8, 3686, 3303337] C213
95) [4632697, 2827, 839808] C3 x C213 ---) [8, 5654, 4632697] C213
96) [4872281, 2491, 333200] C3 x C213 ---) [17, 4982, 4872281] C213
97) [5194649, 2843, 722000] C3 x C213 ---) [5, 4729, 5194649] C213
98) [5545049, 2363, 9680] C3 x C213 ---) [5, 4726, 5545049] C213
99) [6846473, 3075, 652288] C3 x C213 1) [13, 6150, 6846473] C3 x C213
100) [7138217, 2675, 4352] C3 x C213 ---) [17, 5350, 7138217] C213
101) [9165929, 3219, 299008] C3 x C213 5) [73, 6438, 9165929] C3 x C213
102) [9255881, 3747, 1196032] C3 x C213 3) [73, 7494, 9255881] C3 x C213
103) [12569021, 13333, 16161925] C3 x C213 2) [13, 7149, 12569021] C3 x C213
104) [15910649, 4043, 108800] C3 x C213 ---) [17, 8086, 15910649] C213