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 C315 non-normal (D4) quartic CM field invariants: 126 fields

K Quartic invariants Cl(OK) Igusa invariants Kr Reflex invariants Cl(OKr) Igusa invariants
1) [13, 8646, 18125897] C3 x C315 125) [18125897, 4323, 140608] C3 x C315
2) [41, 1702, 534617] C3 x C315 94) [534617, 851, 47396] C3 x C315
3) [229, 869, 184153] C3 x C315 87) [184153, 1738, 18549] C3 x C315
4) [257, 1759, 703552] C3 x C315 ---) [10993, 1159, 333072] C315
5) [257, 1683, 52708] C3 x C315 ---) [13177, 1679, 148032] C315
6) [349, 2441, 1356913] C3 x C315 102) [1356913, 4882, 530829] C3 x C315
7) [733, 974, 131617] C3 x C315 ---) [131617, 487, 26388] C315
8) [1097, 1211, 67972] C3 x C315 67) [16993, 2422, 1194633] C3 x C315
9) [1129, 1983, 745700] C3 x C315 ---) [7457, 2347, 18064] C105
10) [1889, 2175, 48784] C3 x C315 19) [3049, 1539, 188900] C3 x C315
11) [2081, 946, 15629] C3 x C315 ---) [15629, 473, 52025] C3 x C9 x C63
12) [2089, 1759, 760464] C3 x C315 34) [5281, 3175, 300816] C3 x C315
13) [2677, 389, 37161] C3 x C315 ---) [4129, 778, 2677] C315
14) [2677, 5177, 6212449] C3 x C315 ---) [17209, 4451, 267700] C315
15) [2777, 1543, 577856] C3 x C315 ---) [9029, 3086, 69425] C7 x C315
16) [2917, 1733, 50013] C3 x C315 ---) [5557, 3466, 2803237] C315
17) [2917, 4342, 3966489] C3 x C315 ---) [5441, 2171, 186688] C315
18) [3049, 6923, 5102676] C3 x C315 63) [15749, 3605, 2930089] C3 x C315
19) [3049, 1539, 188900] C3 x C315 10) [1889, 2175, 48784] C3 x C315
20) [3137, 1095, 73108] C3 x C315 ---) [373, 557, 28233] C105
21) [3137, 3206, 762697] C3 x C315 ---) [4513, 1603, 451728] C105
22) [3229, 3214, 50913] C3 x C315 ---) [5657, 1607, 632884] C315
23) [3229, 2537, 1569537] C3 x C315 ---) [2153, 2063, 826624] C5 x C315
24) [3673, 487, 51028] C3 x C315 57) [12757, 974, 33057] C3 x C315
25) [3889, 2538, 1221461] C3 x C315 ---) [2309, 1269, 97225] C315
26) [4001, 3506, 368333] C3 x C315 ---) [7517, 1753, 676169] C315
27) [4153, 1643, 623988] C3 x C315 68) [17333, 3286, 203497] C3 x C315
28) [4409, 1683, 19216] C3 x C315 ---) [1201, 1603, 634896] C105
29) [4481, 3311, 266048] C3 x C315 ---) [4157, 4193, 4481] C315
30) [4493, 6170, 10037] C3 x C315 ---) [10037, 3085, 2376797] C315
31) [4729, 6411, 9139088] C3 x C315 ---) [11657, 6091, 4842496] C315
32) [4729, 1875, 537236] C3 x C315 ---) [2741, 3750, 1366681] C315
33) [5009, 6319, 3309200] C3 x C315 45) [8273, 3331, 2424356] C3 x C315
34) [5281, 3175, 300816] C3 x C315 12) [2089, 1759, 760464] C3 x C315
35) [5281, 2883, 1854800] C3 x C315 ---) [4637, 5217, 1906441] C315
36) [5297, 2599, 246592] C3 x C315 ---) [3853, 4689, 640937] C315
37) [5741, 7846, 13093529] C3 x C315 ---) [15569, 3923, 574100] C315
38) [5801, 3530, 1978229] C3 x C315 65) [16349, 1765, 284249] C3 x C315
39) [6133, 1389, 407201] C3 x C315 ---) [1409, 2778, 300517] C315
40) [6637, 1597, 436833] C3 x C315 ---) [5393, 3194, 803077] C315
41) [7057, 1699, 508176] C3 x C315 ---) [3529, 3398, 853897] C45
42) [7537, 4235, 2899152] C3 x C315 ---) [2237, 2297, 1273753] C315
43) [8017, 1379, 136692] C3 x C315 ---) [3797, 2758, 1354873] C315
44) [8069, 2586, 90325] C3 x C315 ---) [3613, 1293, 395381] C315
45) [8273, 3331, 2424356] C3 x C315 33) [5009, 6319, 3309200] C3 x C315
46) [8597, 133, 2273] C3 x C315 ---) [2273, 266, 8597] C315
47) [9413, 4269, 4440781] C3 x C315 ---) [4621, 5753, 2117925] C315
48) [9749, 3309, 1214089] C3 x C315 ---) [4201, 6351, 2495744] C315
49) [9833, 3842, 3336253] C3 x C315 ---) [2437, 1921, 88497] C315
50) [10069, 1233, 317141] C3 x C315 ---) [2621, 2466, 251725] C315
51) [10301, 2373, 1096177] C3 x C315 ---) [3793, 4746, 1246421] C315
52) [10301, 4478, 892721] C3 x C315 ---) [3089, 2239, 1030100] C315
53) [10333, 1181, 36117] C3 x C315 ---) [4013, 2362, 1250293] C315
54) [11057, 6071, 852404] C3 x C315 ---) [4349, 5057, 3991577] C315
55) [11273, 1407, 18628] C3 x C315 ---) [4657, 2814, 1905137] C3 x C63
56) [12301, 1541, 565993] C3 x C315 ---) [673, 3082, 110709] C3 x C63
57) [12757, 974, 33057] C3 x C315 24) [3673, 487, 51028] C3 x C315
58) [14653, 498, 3389] C3 x C315 ---) [3389, 249, 14653] C315
59) [15193, 3683, 3205008] C3 x C315 ---) [2473, 5915, 2187792] C315
60) [15629, 2449, 1495493] C3 x C315 ---) [677, 3349, 2641301] C105
61) [15641, 1391, 448528] C3 x C315 ---) [97, 723, 62564] C315
62) [15661, 2082, 1021037] C3 x C315 ---) [3533, 1041, 15661] C315
63) [15749, 3605, 2930089] C3 x C315 18) [3049, 6923, 5102676] C3 x C315
64) [15773, 5177, 6696389] C3 x C315 ---) [2789, 4357, 394325] C315
65) [16349, 1765, 284249] C3 x C315 38) [5801, 3530, 1978229] C3 x C315
66) [16477, 8373, 2199053] C3 x C315 ---) [4157, 4533, 4761853] C315
67) [16993, 2422, 1194633] C3 x C315 8) [1097, 1211, 67972] C3 x C315
68) [17333, 3286, 203497] C3 x C315 27) [4153, 1643, 623988] C3 x C315
69) [17929, 6314, 4157653] C3 x C315 ---) [3037, 3157, 1452249] C315
70) [19213, 437, 4513] C3 x C315 ---) [4513, 874, 172917] C315
71) [19441, 1126, 5913] C3 x C315 ---) [73, 563, 77764] C105
72) [30553, 551, 7156] C3 x C315 ---) [1789, 1102, 274977] C315
73) [35081, 623, 18100] C3 x C315 ---) [181, 1246, 315729] C3 x C45
74) [40709, 1009, 89] C3 x C315 ---) [89, 1999, 651344] C105
75) [42853, 1501, 552537] C3 x C315 ---) [73, 1259, 171412] C63
76) [56333, 1042, 46109] C3 x C315 ---) [941, 521, 56333] C315
77) [70729, 411, 24548] C3 x C315 ---) [17, 822, 70729] C315
78) [81701, 373, 14357] C3 x C315 ---) [293, 746, 81701] C3 x C45
79) [88337, 1747, 210896] C3 x C315 ---) [269, 3494, 2208425] C315
80) [91801, 1562, 242757] C3 x C315 ---) [37, 781, 91801] C315
81) [101273, 467, 29204] C3 x C315 ---) [149, 934, 101273] C315
82) [118061, 569, 51425] C3 x C315 ---) [17, 1138, 118061] C105
83) [129313, 2926, 71361] C3 x C315 ---) [881, 1463, 517252] C315
84) [150193, 1163, 208] C3 x C315 ---) [13, 893, 150193] C45
85) [161741, 1610, 1061] C3 x C315 ---) [1061, 805, 161741] C315
86) [163741, 889, 156645] C3 x C315 ---) [5, 897, 163741] C45
87) [184153, 1738, 18549] C3 x C315 3) [229, 869, 184153] C3 x C315
88) [267857, 527, 2468] C3 x C315 ---) [617, 1054, 267857] C315
89) [273929, 1123, 246800] C3 x C315 ---) [617, 2246, 273929] C315
90) [318629, 565, 149] C3 x C315 ---) [149, 1130, 318629] C315
91) [502553, 4199, 1266944] C3 x C315 ---) [101, 7661, 12563825] C315
92) [506893, 713, 369] C3 x C315 ---) [41, 1426, 506893] C315
93) [521357, 2890, 2597] C3 x C315 ---) [53, 1445, 521357] C315
94) [534617, 851, 47396] C3 x C315 2) [41, 1702, 534617] C3 x C315
95) [570697, 787, 12168] C3 x C315 ---) [8, 1574, 570697] C63
96) [641881, 1041, 110450] C3 x C315 ---) [8, 2082, 641881] C63
97) [727777, 935, 36612] C3 x C315 ---) [113, 1870, 727777] C315
98) [740053, 3442, 1629] C3 x C315 ---) [181, 1721, 740053] C315
99) [818249, 1193, 151250] C3 x C315 ---) [8, 2386, 818249] C105
100) [1219793, 1335, 140608] C3 x C315 ---) [13, 2670, 1219793] C315
101) [1236953, 1115, 1568] C3 x C315 ---) [8, 2230, 1236953] C63
102) [1356913, 4882, 530829] C3 x C315 6) [349, 2441, 1356913] C3 x C315
103) [1564501, 1253, 1377] C3 x C315 ---) [17, 2506, 1564501] C315
104) [2238961, 2271, 729620] C3 x C315 ---) [5, 2993, 2238961] C315
105) [2366537, 2403, 851968] C3 x C315 ---) [13, 4806, 2366537] C315
106) [2548361, 2371, 768320] C3 x C315 ---) [5, 3193, 2548361] C315
107) [2569529, 1603, 20] C3 x C315 ---) [5, 3206, 2569529] C3 x C63
108) [3280657, 5435, 3328] C3 x C315 ---) [13, 4181, 3280657] C315
109) [3484001, 1999, 128000] C3 x C315 ---) [5, 3998, 3484001] C315
110) [3551209, 2667, 890420] C3 x C315 ---) [5, 3781, 3551209] C315
111) [3862609, 1967, 1620] C3 x C315 ---) [5, 3934, 3862609] C315
112) [3977929, 2339, 373248] C3 x C315 ---) [8, 4678, 3977929] C315
113) [4074313, 7055, 3276052] C3 x C315 ---) [13, 4037, 4074313] C315
114) [4139129, 3043, 1280180] C3 x C315 ---) [5, 4069, 4139129] C315
115) [5887769, 2683, 327680] C3 x C315 ---) [5, 5366, 5887769] C315
116) [6104009, 2723, 327680] C3 x C315 ---) [5, 5446, 6104009] C315
117) [6741569, 2783, 250880] C3 x C315 ---) [5, 5566, 6741569] C315
118) [7626337, 2767, 7488] C3 x C315 ---) [13, 5534, 7626337] C315
119) [8334553, 2891, 5832] C3 x C315 ---) [8, 5782, 8334553] C315
120) [9156209, 3047, 32000] C3 x C315 ---) [5, 6094, 9156209] C315
121) [9949417, 3155, 1152] C3 x C315 ---) [8, 6310, 9949417] C315
122) [10805177, 3307, 32768] C3 x C315 ---) [8, 6614, 10805177] C315
123) [11728217, 3547, 213248] C3 x C315 ---) [17, 7094, 11728217] C315
124) [14439881, 4259, 924800] C3 x C315 ---) [8, 8518, 14439881] C315
125) [18125897, 4323, 140608] C3 x C315 1) [13, 8646, 18125897] C3 x C315
126) [28843721, 5411, 108800] C3 x C315 ---) [17, 10822, 28843721] C315