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 C865 non-normal (D4) quartic CM field invariants: 121 fields

K Quartic invariants Cl(OK) Igusa invariants Kr Reflex invariants Cl(OKr) Igusa invariants
1) [8, 6014, 9040897] C865 121) [9040897, 3007, 288] C865
2) [17, 2494, 1276481] C865 110) [1276481, 1247, 69632] C865
3) [17, 2782, 1895713] C865 114) [1895713, 1391, 9792] C865
4) [29, 3214, 2515633] C865 118) [2515633, 1607, 16704] C865
5) [37, 3678, 3322721] C865 119) [3322721, 1839, 14800] C865
6) [37, 3510, 3070553] C865 ---) [3070553, 1755, 2368] C7785
7) [61, 3702, 2016857] C865 115) [2016857, 1851, 352336] C865
8) [97, 4558, 5038641] C865 103) [559849, 2279, 38800] C865
9) [101, 3814, 3475049] C865 120) [3475049, 1907, 40400] C865
10) [109, 2598, 1345577] C865 111) [1345577, 1299, 85456] C865
11) [109, 3414, 1127993] C865 108) [1127993, 1707, 446464] C865
12) [193, 4662, 5124761] C865 ---) [5124761, 2331, 77200] C5 x C865
13) [233, 462, 38449] C865 92) [38449, 231, 3728] C865
14) [293, 2582, 747833] C865 ---) [747833, 1291, 229712] C6055
15) [353, 1594, 633797] C865 105) [633797, 797, 353] C865
16) [461, 1366, 459113] C865 102) [459113, 683, 1844] C865
17) [661, 1509, 561173] C865 104) [561173, 3018, 32389] C865
18) [797, 1325, 351037] C865 100) [351037, 2650, 351477] C865
19) [1093, 285, 6917] C865 ---) [6917, 570, 53557] C173
20) [1117, 630, 81353] C865 93) [81353, 315, 4468] C865
21) [1117, 713, 113409] C865 77) [12601, 1426, 54733] C865
22) [1409, 3082, 2233781] C865 87) [18461, 1541, 35225] C865
23) [1553, 1167, 340084] C865 ---) [85021, 2334, 1553] C2595
24) [1669, 981, 240173] C865 98) [240173, 1962, 1669] C865
25) [1933, 825, 146477] C865 95) [146477, 1650, 94717] C865
26) [2069, 1254, 360025] C865 ---) [14401, 627, 8276] C37195
27) [2081, 2914, 249949] C865 ---) [5101, 1457, 468225] C173
28) [2269, 1150, 3889] C865 ---) [3889, 575, 81684] C2595
29) [2417, 1623, 483904] C865 68) [7561, 3246, 698513] C865
30) [2417, 651, 32836] C865 71) [8209, 1302, 292457] C865
31) [2593, 1855, 672912] C865 54) [4673, 3267, 508228] C865
32) [2609, 2479, 1504400] C865 42) [3761, 2051, 260900] C865
33) [3041, 1935, 205456] C865 78) [12841, 3870, 2922401] C865
34) [3121, 6215, 3476196] C865 ---) [10729, 3887, 2808900] C173
35) [3169, 838, 124857] C865 80) [13873, 419, 12676] C865
36) [3209, 6951, 6552400] C865 82) [16381, 3785, 1415169] C865
37) [3253, 2553, 1492013] C865 ---) [4133, 3629, 1720837] C173
38) [3253, 437, 7893] C865 ---) [877, 874, 159397] C173
39) [3433, 4718, 72081] C865 69) [8009, 2359, 1373200] C865
40) [3457, 3391, 66772] C865 83) [16693, 6782, 11231793] C865
41) [3761, 5167, 3619600] C865 ---) [9049, 3471, 240704] C6055
42) [3761, 2051, 260900] C865 32) [2609, 2479, 1504400] C865
43) [3793, 5063, 187024] C865 76) [11689, 4591, 4915728] C865
44) [3833, 6882, 2257981] C865 ---) [18661, 3441, 2395625] C2595
45) [3929, 7498, 2598037] C865 81) [15373, 3749, 2864241] C865
46) [4049, 2154, 366325] C865 ---) [14653, 1077, 198401] C2595
47) [4129, 5563, 625572] C865 85) [17377, 7879, 2378304] C865
48) [4261, 2761, 1521225] C865 66) [6761, 5522, 1538221] C865
49) [4273, 3226, 2447941] C865 67) [6781, 1613, 38457] C865
50) [4289, 4955, 1033024] C865 ---) [16141, 8553, 1239521] C2595
51) [4357, 482, 40653] C865 ---) [4517, 241, 4357] C173
52) [4441, 859, 130068] C865 ---) [3613, 1718, 217609] C173
53) [4441, 7027, 8986176] C865 ---) [15601, 8123, 8597776] C173
54) [4673, 3267, 508228] C865 31) [2593, 1855, 672912] C865
55) [4889, 842, 1237] C865 ---) [1237, 421, 44001] C173
56) [5113, 2338, 1182493] C865 ---) [6997, 1169, 46017] C2595
57) [5189, 3549, 283225] C865 75) [11329, 7098, 11462501] C865
58) [5197, 6829, 9880137] C865 79) [13553, 5415, 4074448] C865
59) [5381, 4566, 5125993] C865 ---) [17737, 2283, 21524] C5 x C2595
60) [5413, 7853, 6971769] C865 ---) [15809, 8571, 3659188] C6055
61) [5449, 3023, 2250576] C865 ---) [15629, 6046, 136225] C7785
62) [5449, 4423, 3897652] C865 70) [8053, 5633, 441369] C865
63) [5557, 8609, 155889] C865 84) [17321, 6507, 6423892] C865
64) [5693, 4137, 1886209] C865 74) [11161, 7951, 3279168] C865
65) [5701, 9861, 16714673] C865 86) [17393, 5127, 3853876] C865
66) [6761, 5522, 1538221] C865 48) [4261, 2761, 1521225] C865
67) [6781, 1613, 38457] C865 49) [4273, 3226, 2447941] C865
68) [7561, 3246, 698513] C865 29) [2417, 1623, 483904] C865
69) [8009, 2359, 1373200] C865 39) [3433, 4718, 72081] C865
70) [8053, 5633, 441369] C865 62) [5449, 4423, 3897652] C865
71) [8209, 1302, 292457] C865 30) [2417, 651, 32836] C865
72) [8501, 697, 102325] C865 ---) [4093, 1394, 76509] C173
73) [8689, 3099, 2346644] C865 ---) [1109, 2585, 1468441] C173
74) [11161, 7951, 3279168] C865 64) [5693, 4137, 1886209] C865
75) [11329, 7098, 11462501] C865 57) [5189, 3549, 283225] C865
76) [11689, 4591, 4915728] C865 43) [3793, 5063, 187024] C865
77) [12601, 1426, 54733] C865 21) [1117, 713, 113409] C865
78) [12841, 3870, 2922401] C865 33) [3041, 1935, 205456] C865
79) [13553, 5415, 4074448] C865 58) [5197, 6829, 9880137] C865
80) [13873, 419, 12676] C865 35) [3169, 838, 124857] C865
81) [15373, 3749, 2864241] C865 45) [3929, 7498, 2598037] C865
82) [16381, 3785, 1415169] C865 36) [3209, 6951, 6552400] C865
83) [16693, 6782, 11231793] C865 40) [3457, 3391, 66772] C865
84) [17321, 6507, 6423892] C865 63) [5557, 8609, 155889] C865
85) [17377, 7879, 2378304] C865 47) [4129, 5563, 625572] C865
86) [17393, 5127, 3853876] C865 65) [5701, 9861, 16714673] C865
87) [18461, 1541, 35225] C865 22) [1409, 3082, 2233781] C865
88) [25153, 2099, 38736] C865 ---) [269, 1841, 628825] C173
89) [30893, 2822, 13769] C865 ---) [281, 1411, 494288] C173
90) [37781, 778, 197] C865 ---) [197, 389, 37781] C173
91) [38177, 1946, 794021] C865 ---) [149, 973, 38177] C173
92) [38449, 231, 3728] C865 13) [233, 462, 38449] C865
93) [81353, 315, 4468] C865 20) [1117, 630, 81353] C865
94) [87257, 379, 14096] C865 ---) [881, 758, 87257] C173
95) [146477, 1650, 94717] C865 25) [1933, 825, 146477] C865
96) [197389, 449, 1053] C865 ---) [13, 898, 197389] C173
97) [239053, 489, 17] C865 ---) [17, 978, 239053] C173
98) [240173, 1962, 1669] C865 24) [1669, 981, 240173] C865
99) [350549, 757, 55625] C865 ---) [89, 1514, 350549] C173
100) [351037, 2650, 351477] C865 18) [797, 1325, 351037] C865
101) [361789, 833, 83025] C865 ---) [41, 1666, 361789] C173
102) [459113, 683, 1844] C865 16) [461, 1366, 459113] C865
103) [559849, 2279, 38800] C865 8) [97, 4558, 5038641] C865
104) [561173, 3018, 32389] C865 17) [661, 1509, 561173] C865
105) [633797, 797, 353] C865 15) [353, 1594, 633797] C865
106) [793673, 891, 52] C865 ---) [13, 1782, 793673] C173
107) [1031741, 1017, 637] C865 ---) [13, 2034, 1031741] C173
108) [1127993, 1707, 446464] C865 11) [109, 3414, 1127993] C865
109) [1169401, 1123, 22932] C865 ---) [13, 2246, 1169401] C173
110) [1276481, 1247, 69632] C865 2) [17, 2494, 1276481] C865
111) [1345577, 1299, 85456] C865 10) [109, 2598, 1345577] C865
112) [1533101, 1889, 508805] C865 ---) [5, 2477, 1533101] C173
113) [1815817, 4055, 25168] C865 ---) [13, 3281, 1815817] C173
114) [1895713, 1391, 9792] C865 3) [17, 2782, 1895713] C865
115) [2016857, 1851, 352336] C865 7) [61, 3702, 2016857] C865
116) [2436341, 1661, 80645] C865 ---) [5, 3322, 2436341] C173
117) [2513941, 3021, 1653125] C865 ---) [5, 3313, 2513941] C173
118) [2515633, 1607, 16704] C865 4) [29, 3214, 2515633] C865
119) [3322721, 1839, 14800] C865 5) [37, 3678, 3322721] C865
120) [3475049, 1907, 40400] C865 9) [101, 3814, 3475049] C865
121) [9040897, 3007, 288] C865 1) [8, 6014, 9040897] C865