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 C975 non-normal (D4) quartic CM field invariants: 138 fields

K Quartic invariants Cl(OK) Igusa invariants Kr Reflex invariants Cl(OKr) Igusa invariants
1) [5, 9406, 21800689] C975 ---) [21800689, 4703, 79380] C3 x C975
2) [8, 3790, 3365233] C975 128) [3365233, 1895, 56448] C975
3) [8, 5534, 7283041] C975 ---) [7283041, 2767, 93312] C6825
4) [13, 5598, 7501601] C975 ---) [7501601, 2799, 83200] C16575
5) [17, 2798, 1825553] C975 124) [1825553, 1399, 32912] C975
6) [29, 5686, 8052953] C975 ---) [8052953, 2843, 7424] C5 x C975
7) [29, 4606, 5079233] C975 134) [5079233, 2303, 56144] C975
8) [37, 4374, 4773497] C975 132) [4773497, 2187, 2368] C975
9) [41, 2510, 1572401] C975 123) [1572401, 1255, 656] C975
10) [61, 4566, 4552313] C975 130) [4552313, 2283, 164944] C975
11) [101, 3758, 2748497] C975 127) [2748497, 1879, 195536] C975
12) [181, 1422, 493937] C975 113) [493937, 711, 2896] C975
13) [229, 390, 23369] C975 ---) [23369, 195, 3664] C325
14) [229, 2150, 1023721] C975 120) [1023721, 1075, 32976] C975
15) [269, 2534, 1588073] C975 ---) [1588073, 1267, 4304] C3 x C975
16) [269, 2990, 1391441] C975 121) [1391441, 1495, 210896] C975
17) [277, 1782, 510233] C975 114) [510233, 891, 70912] C975
18) [277, 2870, 1899673] C975 125) [1899673, 1435, 39888] C975
19) [281, 646, 99833] C975 ---) [99833, 323, 1124] C5 x C975
20) [293, 2846, 824801] C975 117) [824801, 1423, 300032] C975
21) [349, 3958, 2821977] C975 ---) [313553, 1979, 273616] C3 x C975
22) [353, 670, 89633] C975 104) [89633, 335, 5648] C975
23) [389, 2998, 1027097] C975 ---) [1027097, 1499, 304976] C3 x C975
24) [409, 2622, 43457] C975 100) [43457, 1311, 418816] C975
25) [557, 1414, 490937] C975 112) [490937, 707, 2228] C975
26) [821, 1022, 208577] C975 ---) [208577, 511, 13136] C10725
27) [821, 974, 224033] C975 106) [224033, 487, 3284] C975
28) [953, 2231, 1070656] C975 87) [16729, 3759, 15248] C975
29) [977, 782, 90353] C975 105) [90353, 391, 15632] C975
30) [1097, 683, 54916] C975 78) [13729, 1366, 246825] C975
31) [1321, 1063, 136852] C975 97) [34213, 2126, 582561] C975
32) [1433, 4278, 1801033] C975 75) [10657, 2139, 693572] C975
33) [1609, 1526, 556425] C975 37) [2473, 763, 6436] C975
34) [1973, 957, 228469] C975 107) [228469, 1914, 1973] C975
35) [2089, 754, 66925] C975 40) [2677, 377, 18801] C975
36) [2161, 615, 68084] C975 88) [17021, 1230, 105889] C975
37) [2473, 763, 6436] C975 33) [1609, 1526, 556425] C975
38) [2473, 910, 48753] C975 ---) [5417, 455, 39568] C6825
39) [2633, 2086, 708697] C975 66) [5857, 1043, 94788] C975
40) [2677, 377, 18801] C975 35) [2089, 754, 66925] C975
41) [2689, 1219, 75028] C975 95) [18757, 2438, 1185849] C975
42) [2689, 1507, 271300] C975 ---) [2713, 2627, 96804] C3 x C975
43) [2749, 5794, 376525] C975 ---) [15061, 2897, 2004021] C3 x C975
44) [2753, 1851, 13444] C975 46) [3361, 2551, 1585728] C975
45) [3169, 1694, 514593] C975 68) [6353, 847, 50704] C975
46) [3361, 2551, 1585728] C975 44) [2753, 1851, 13444] C975
47) [3673, 3691, 628164] C975 89) [17449, 7382, 11110825] C975
48) [3673, 2491, 1506276] C975 ---) [4649, 3511, 58768] C3 x C975
49) [4241, 6315, 3683584] C975 ---) [14389, 4865, 4618449] C3 x C975
50) [4253, 2581, 890281] C975 92) [18169, 5162, 3100437] C975
51) [4297, 7351, 4218112] C975 ---) [16477, 5389, 7223257] C3 x C975
52) [4493, 3577, 2946001] C975 ---) [5569, 3667, 1455732] C325
53) [4493, 842, 15493] C975 ---) [15493, 421, 40437] C325
54) [4813, 6250, 9592357] C975 91) [18133, 3125, 43317] C975
55) [5009, 5126, 6488825] C975 ---) [5297, 2563, 20036] C3 x C975
56) [5009, 4118, 312425] C975 ---) [12497, 2059, 981764] C6825
57) [5333, 898, 9613] C975 ---) [9613, 449, 47997] C325
58) [5333, 181, 6857] C975 ---) [6857, 362, 5333] C325
59) [5333, 253, 14669] C975 ---) [14669, 506, 5333] C325
60) [5437, 3254, 1255257] C975 83) [15497, 1627, 347968] C975
61) [5477, 5113, 16693] C975 ---) [16693, 9697, 17794773] C325
62) [5701, 7062, 10187561] C975 74) [10601, 3531, 570100] C975
63) [5701, 9869, 4166325] C975 93) [18517, 5677, 3015829] C975
64) [5701, 3113, 2181825] C975 71) [9697, 6226, 963469] C975
65) [5737, 1971, 74804] C975 ---) [18701, 3942, 3585625] C3 x C975
66) [5857, 1043, 94788] C975 39) [2633, 2086, 708697] C975
67) [5953, 7463, 6421824] C975 76) [11149, 4541, 1339425] C975
68) [6353, 847, 50704] C975 45) [3169, 1694, 514593] C975
69) [7481, 806, 42713] C975 ---) [353, 403, 29924] C325
70) [8581, 5173, 6687837] C975 ---) [4397, 4917, 4539349] C325
71) [9697, 6226, 963469] C975 64) [5701, 3113, 2181825] C975
72) [10457, 2579, 279872] C975 ---) [4373, 5158, 5531753] C325
73) [10457, 1367, 150848] C975 ---) [2357, 2734, 1265297] C325
74) [10601, 3531, 570100] C975 62) [5701, 7062, 10187561] C975
75) [10657, 2139, 693572] C975 32) [1433, 4278, 1801033] C975
76) [11149, 4541, 1339425] C975 67) [5953, 7463, 6421824] C975
77) [12821, 2013, 86725] C975 ---) [3469, 4026, 3705269] C325
78) [13729, 1366, 246825] C975 30) [1097, 683, 54916] C975
79) [13877, 6098, 2579933] C975 ---) [4877, 3049, 1679117] C325
80) [14197, 2137, 712233] C975 ---) [977, 3531, 2782612] C325
81) [14969, 930, 156349] C975 ---) [541, 465, 14969] C325
82) [15377, 1379, 10256] C975 ---) [641, 2758, 1860617] C75
83) [15497, 1627, 347968] C975 60) [5437, 3254, 1255257] C975
84) [15733, 3473, 1595529] C975 ---) [1049, 2583, 1573300] C325
85) [15737, 1647, 13264] C975 ---) [829, 3294, 2659553] C325
86) [16369, 2771, 1424448] C975 ---) [2473, 5542, 1980649] C325
87) [16729, 3759, 15248] C975 28) [953, 2231, 1070656] C975
88) [17021, 1230, 105889] C975 36) [2161, 615, 68084] C975
89) [17449, 7382, 11110825] C975 47) [3673, 3691, 628164] C975
90) [17929, 2179, 1182528] C975 ---) [2053, 4358, 17929] C325
91) [18133, 3125, 43317] C975 54) [4813, 6250, 9592357] C975
92) [18169, 5162, 3100437] C975 50) [4253, 2581, 890281] C975
93) [18517, 5677, 3015829] C975 63) [5701, 9869, 4166325] C975
94) [18701, 2478, 338257] C975 ---) [937, 1239, 299216] C325
95) [18757, 2438, 1185849] C975 41) [2689, 1219, 75028] C975
96) [33301, 1357, 52425] C975 ---) [233, 2714, 1631749] C325
97) [34213, 2126, 582561] C975 31) [1321, 1063, 136852] C975
98) [37489, 1798, 208377] C975 ---) [137, 899, 149956] C325
99) [39733, 2458, 80053] C975 ---) [277, 1229, 357597] C325
100) [43457, 1311, 418816] C975 24) [409, 2622, 43457] C975
101) [55073, 551, 62132] C975 ---) [317, 1102, 55073] C325
102) [74933, 1218, 71149] C975 ---) [421, 609, 74933] C325
103) [75869, 281, 773] C975 ---) [773, 562, 75869] C325
104) [89633, 335, 5648] C975 22) [353, 670, 89633] C975
105) [90353, 391, 15632] C975 29) [977, 782, 90353] C975
106) [224033, 487, 3284] C975 27) [821, 974, 224033] C975
107) [228469, 1914, 1973] C975 34) [1973, 957, 228469] C975
108) [245317, 565, 18477] C975 ---) [2053, 1130, 245317] C325
109) [345749, 589, 293] C975 ---) [293, 1178, 345749] C325
110) [427433, 1779, 684352] C975 ---) [37, 3558, 427433] C325
111) [448193, 1055, 166208] C975 ---) [53, 2110, 448193] C325
112) [490937, 707, 2228] C975 25) [557, 1414, 490937] C975
113) [493937, 711, 2896] C975 12) [181, 1422, 493937] C975
114) [510233, 891, 70912] C975 17) [277, 1782, 510233] C975
115) [522073, 827, 40464] C975 ---) [281, 1654, 522073] C325
116) [595277, 809, 14801] C975 ---) [41, 1618, 595277] C325
117) [824801, 1423, 300032] C975 20) [293, 2846, 824801] C975
118) [929561, 1115, 78416] C975 ---) [29, 2230, 929561] C325
119) [953041, 1029, 26450] C975 ---) [8, 2058, 953041] C325
120) [1023721, 1075, 32976] C975 14) [229, 2150, 1023721] C975
121) [1391441, 1495, 210896] C975 16) [269, 2990, 1391441] C975
122) [1434217, 1811, 461376] C975 ---) [89, 3622, 1434217] C325
123) [1572401, 1255, 656] C975 9) [41, 2510, 1572401] C975
124) [1825553, 1399, 32912] C975 5) [17, 2798, 1825553] C975
125) [1899673, 1435, 39888] C975 18) [277, 2870, 1899673] C975
126) [2330473, 2707, 1249344] C975 ---) [241, 5414, 2330473] C325
127) [2748497, 1879, 195536] C975 11) [101, 3758, 2748497] C975
128) [3365233, 1895, 56448] C975 2) [8, 3790, 3365233] C975
129) [4252393, 2483, 478224] C975 ---) [41, 4966, 4252393] C325
130) [4552313, 2283, 164944] C975 10) [61, 4566, 4552313] C975
131) [4622561, 2159, 9680] C975 ---) [5, 4318, 4622561] C325
132) [4773497, 2187, 2368] C975 8) [37, 4374, 4773497] C975
133) [4826729, 2323, 142400] C975 ---) [89, 4646, 4826729] C325
134) [5079233, 2303, 56144] C975 7) [29, 4606, 5079233] C975
135) [7971913, 2825, 2178] C975 ---) [8, 5650, 7971913] C325
136) [9544009, 4003, 1620000] C975 ---) [8, 8006, 9544009] C325
137) [16220249, 4187, 327680] C975 ---) [5, 8374, 16220249] C325
138) [16999673, 4139, 32912] C975 ---) [17, 8278, 16999673] C325