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 C895 non-normal (D4) quartic CM field invariants: 88 fields

K Quartic invariants Cl(OK) Igusa invariants Kr Reflex invariants Cl(OKr) Igusa invariants
1) [8, 5950, 8849473] C895 88) [8849473, 2975, 288] C895
2) [13, 5502, 7484801] C895 ---) [7484801, 2751, 20800] C5 x C895
3) [17, 1918, 909889] C895 ---) [909889, 959, 2448] C5 x C27745
4) [17, 3358, 1078241] C895 76) [1078241, 1679, 435200] C895
5) [29, 4342, 4527641] C895 ---) [4527641, 2171, 46400] C5 x C2685
6) [29, 4718, 5548177] C895 84) [5548177, 2359, 4176] C895
7) [29, 5782, 8350457] C895 87) [8350457, 2891, 1856] C895
8) [37, 4086, 3027737] C895 80) [3027737, 2043, 286528] C895
9) [53, 1982, 951553] C895 75) [951553, 991, 7632] C895
10) [53, 3950, 3887057] C895 81) [3887057, 1975, 3392] C895
11) [53, 4270, 4503953] C895 83) [4503953, 2135, 13568] C895
12) [337, 1711, 725056] C895 53) [11329, 1207, 134800] C895
13) [389, 1222, 149257] C895 ---) [149257, 611, 56016] C8055
14) [401, 746, 137525] C895 ---) [5501, 373, 401] C179
15) [401, 1050, 4549] C895 ---) [4549, 525, 67769] C179
16) [449, 574, 53633] C895 ---) [53633, 287, 7184] C2685
17) [641, 294, 11353] C895 54) [11353, 147, 2564] C895
18) [857, 898, 170749] C895 71) [170749, 449, 7713] C895
19) [1069, 1017, 245477] C895 ---) [245477, 2034, 52381] C8055
20) [1093, 738, 26861] C895 ---) [26861, 369, 27325] C179
21) [1093, 3182, 13009] C895 ---) [13009, 1591, 629568] C179
22) [1097, 515, 52868] C895 58) [13217, 1030, 53753] C895
23) [1433, 1487, 113936] C895 48) [7121, 2974, 1755425] C895
24) [1657, 982, 2473] C895 30) [2473, 491, 59652] C895
25) [1733, 817, 162973] C895 70) [162973, 1634, 15597] C895
26) [2069, 869, 146893] C895 69) [146893, 1738, 167589] C895
27) [2137, 2194, 511021] C895 50) [10429, 1097, 173097] C895
28) [2161, 2375, 821824] C895 57) [12841, 4750, 2353329] C895
29) [2297, 791, 151252] C895 67) [37813, 1582, 20673] C895
30) [2473, 491, 59652] C895 24) [1657, 982, 2473] C895
31) [3121, 4510, 4635601] C895 ---) [12841, 2255, 112356] C179
32) [3449, 5979, 7032400] C895 ---) [17581, 6765, 3314489] C2685
33) [3593, 1679, 49936] C895 ---) [3121, 3358, 2619297] C5 x C895
34) [3637, 5053, 5393029] C895 ---) [18661, 7897, 13533277] C2685
35) [3761, 1107, 192592] C895 55) [12037, 2214, 455081] C895
36) [3881, 8191, 6875600] C895 65) [17189, 7549, 4754225] C895
37) [4049, 3891, 261328] C895 ---) [16333, 7782, 14094569] C9845
38) [4153, 1167, 165008] C895 ---) [10313, 2334, 701857] C6265
39) [4337, 3719, 3456656] C895 ---) [4409, 3263, 1734800] C8055
40) [4357, 3897, 4973] C895 ---) [4973, 3233, 1259173] C179
41) [4877, 7854, 7618129] C895 ---) [14401, 3927, 1950800] C38485
42) [4909, 7837, 1303857] C895 62) [16097, 5091, 5026816] C895
43) [4909, 4657, 4085437] C895 52) [11317, 6877, 593989] C895
44) [5437, 910, 120033] C895 59) [13337, 455, 21748] C895
45) [5669, 2605, 1695089] C895 ---) [14009, 5210, 5669] C9845
46) [5861, 1893, 894397] C895 ---) [18253, 3786, 5861] C5 x C895
47) [5869, 8798, 3481425] C895 ---) [15473, 4399, 3967444] C5 x C895
48) [7121, 2974, 1755425] C895 23) [1433, 1487, 113936] C895
49) [8689, 2927, 1514052] C895 ---) [4673, 5854, 2511121] C179
50) [10429, 1097, 173097] C895 27) [2137, 2194, 511021] C895
51) [10909, 857, 49977] C895 ---) [617, 1714, 534541] C179
52) [11317, 6877, 593989] C895 43) [4909, 4657, 4085437] C895
53) [11329, 1207, 134800] C895 12) [337, 1711, 725056] C895
54) [11353, 147, 2564] C895 17) [641, 294, 11353] C895
55) [12037, 2214, 455081] C895 35) [3761, 1107, 192592] C895
56) [12301, 2481, 650093] C895 ---) [773, 2429, 12301] C179
57) [12841, 4750, 2353329] C895 28) [2161, 2375, 821824] C895
58) [13217, 1030, 53753] C895 22) [1097, 515, 52868] C895
59) [13337, 455, 21748] C895 44) [5437, 910, 120033] C895
60) [15473, 1619, 1556] C895 ---) [389, 1937, 758177] C179
61) [15473, 2902, 1115129] C895 ---) [3089, 1451, 247568] C179
62) [16097, 5091, 5026816] C895 42) [4909, 7837, 1303857] C895
63) [16741, 698, 54837] C895 ---) [677, 349, 16741] C179
64) [16741, 3949, 1282869] C895 ---) [2909, 6981, 820309] C179
65) [17189, 7549, 4754225] C895 36) [3881, 8191, 6875600] C895
66) [18353, 778, 77909] C895 ---) [461, 389, 18353] C179
67) [37813, 1582, 20673] C895 29) [2297, 791, 151252] C895
68) [119569, 1211, 97600] C895 ---) [61, 2422, 1076121] C179
69) [146893, 1738, 167589] C895 26) [2069, 869, 146893] C895
70) [162973, 1634, 15597] C895 25) [1733, 817, 162973] C895
71) [170749, 449, 7713] C895 18) [857, 898, 170749] C895
72) [322057, 611, 12816] C895 ---) [89, 1222, 322057] C179
73) [376949, 709, 31433] C895 ---) [17, 1418, 376949] C179
74) [751613, 881, 6137] C895 ---) [17, 1762, 751613] C179
75) [951553, 991, 7632] C895 9) [53, 1982, 951553] C895
76) [1078241, 1679, 435200] C895 4) [17, 3358, 1078241] C895
77) [1768937, 1331, 656] C895 ---) [41, 2662, 1768937] C179
78) [2188489, 1667, 147600] C895 ---) [41, 3334, 2188489] C179
79) [2987969, 2687, 1058000] C895 ---) [5, 3461, 2987969] C179
80) [3027737, 2043, 286528] C895 8) [37, 4086, 3027737] C895
81) [3887057, 1975, 3392] C895 10) [53, 3950, 3887057] C895
82) [3976289, 3503, 2073680] C895 ---) [5, 4069, 3976289] C179
83) [4503953, 2135, 13568] C895 11) [53, 4270, 4503953] C895
84) [5548177, 2359, 4176] C895 6) [29, 4718, 5548177] C895
85) [5892937, 3235, 1143072] C895 ---) [8, 6470, 5892937] C179
86) [7647193, 2971, 294912] C895 ---) [8, 5942, 7647193] C179
87) [8350457, 2891, 1856] C895 7) [29, 5782, 8350457] C895
88) [8849473, 2975, 288] C895 1) [8, 5950, 8849473] C895