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 C255 non-normal (D4) quartic CM field invariants: 97 fields

K Quartic invariants Cl(OK) Igusa invariants Kr Reflex invariants Cl(OKr) Igusa invariants
1) [149, 4046, 3138929] C3 x C255 90) [3138929, 2023, 238400] C3 x C255
2) [257, 578, 33149] C3 x C255 ---) [33149, 289, 12593] C255
3) [257, 754, 91757] C3 x C255 ---) [91757, 377, 12593] C255
4) [257, 394, 37781] C3 x C255 ---) [37781, 197, 257] C5 x C255
5) [257, 4390, 607337] C3 x C255 81) [607337, 2195, 1052672] C3 x C255
6) [617, 1274, 403301] C3 x C255 77) [403301, 637, 617] C3 x C255
7) [733, 1901, 837297] C3 x C255 ---) [10337, 2595, 750592] C255
8) [1609, 951, 177428] C3 x C255 ---) [44357, 1902, 194689] C3 x C3 x C255
9) [2089, 1766, 478873] C3 x C255 ---) [1657, 883, 75204] C255
10) [2213, 3349, 15017] C3 x C255 ---) [15017, 6499, 2266112] C255
11) [2213, 370, 25373] C3 x C255 ---) [25373, 185, 2213] C255
12) [2297, 3043, 35764] C3 x C255 39) [8941, 3573, 2813825] C3 x C255
13) [2437, 641, 87489] C3 x C255 42) [9721, 1282, 60925] C3 x C255
14) [2657, 1895, 546368] C3 x C255 37) [8537, 3790, 1405553] C3 x C255
15) [2777, 4010, 10037] C3 x C255 ---) [10037, 2005, 1002497] C255
16) [2777, 1327, 433984] C3 x C255 ---) [6781, 2654, 24993] C255
17) [2857, 2135, 161748] C3 x C255 25) [4493, 3053, 1511353] C3 x C255
18) [2917, 410, 30357] C3 x C255 ---) [3373, 205, 2917] C255
19) [2917, 2865, 3593] C3 x C255 ---) [3593, 2215, 571732] C255
20) [3221, 1257, 297577] C3 x C255 ---) [6073, 2514, 389741] C255
21) [3833, 2255, 1109312] C3 x C255 63) [17333, 4510, 647777] C3 x C255
22) [3853, 1222, 126729] C3 x C255 50) [14081, 611, 61648] C3 x C255
23) [4001, 2559, 1107988] C3 x C255 ---) [5653, 4421, 1764441] C255
24) [4001, 2074, 675269] C3 x C255 ---) [13781, 1037, 100025] C255
25) [4493, 3053, 1511353] C3 x C255 17) [2857, 2135, 161748] C3 x C255
26) [4493, 229, 3001] C3 x C255 ---) [3001, 458, 40437] C255
27) [4493, 2686, 6449] C3 x C255 ---) [6449, 1343, 449300] C255
28) [4597, 2797, 23913] C3 x C255 ---) [2657, 2691, 901012] C255
29) [4649, 2198, 17657] C3 x C255 ---) [17657, 1099, 297536] C255
30) [4861, 7089, 11395625] C3 x C255 65) [18233, 9483, 22477264] C3 x C255
31) [5009, 4514, 2669693] C3 x C255 54) [15797, 2257, 606089] C3 x C255
32) [5297, 1463, 152384] C3 x C255 ---) [2381, 2926, 1530833] C255
33) [5741, 3946, 11813] C3 x C255 ---) [11813, 1973, 970229] C255
34) [6053, 630, 2377] C3 x C255 ---) [2377, 315, 24212] C255
35) [7537, 3271, 1497204] C3 x C255 ---) [4621, 5593, 610497] C255
36) [7817, 155, 4052] C3 x C255 ---) [1013, 310, 7817] C3 x C51
37) [8537, 3790, 1405553] C3 x C255 14) [2657, 1895, 546368] C3 x C255
38) [8837, 5498, 3279893] C3 x C255 ---) [3413, 2749, 1069277] C255
39) [8941, 3573, 2813825] C3 x C255 12) [2297, 3043, 35764] C3 x C255
40) [9133, 2605, 1675957] C3 x C255 ---) [997, 1769, 82197] C255
41) [9413, 3989, 2507249] C3 x C255 ---) [2609, 3211, 150608] C255
42) [9721, 1282, 60925] C3 x C255 13) [2437, 641, 87489] C3 x C255
43) [11057, 975, 102208] C3 x C255 ---) [1597, 1950, 541793] C255
44) [11057, 2011, 13136] C3 x C255 ---) [821, 3133, 276425] C255
45) [11821, 5173, 5623137] C3 x C255 ---) [3697, 5483, 2316916] C255
46) [12401, 2903, 1855732] C3 x C255 ---) [877, 2013, 607649] C255
47) [13693, 2353, 1216413] C3 x C255 ---) [1117, 3317, 13693] C51
48) [13693, 281, 16317] C3 x C255 ---) [37, 562, 13693] C51
49) [13877, 173, 4013] C3 x C255 ---) [4013, 346, 13877] C255
50) [14081, 611, 61648] C3 x C255 22) [3853, 1222, 126729] C3 x C255
51) [14389, 650, 48069] C3 x C255 ---) [109, 325, 14389] C255
52) [15061, 1409, 40725] C3 x C255 ---) [181, 1025, 135549] C255
53) [15661, 1522, 15325] C3 x C255 ---) [613, 761, 140949] C255
54) [15797, 2257, 606089] C3 x C255 31) [5009, 4514, 2669693] C3 x C255
55) [16141, 1782, 535625] C3 x C255 ---) [857, 891, 64564] C255
56) [16477, 3221, 777121] C3 x C255 ---) [2689, 6442, 7266357] C255
57) [16481, 643, 356] C3 x C255 ---) [89, 1286, 412025] C255
58) [16649, 751, 36944] C3 x C255 ---) [2309, 1502, 416225] C255
59) [16661, 4334, 430673] C3 x C255 ---) [1193, 2167, 1066304] C255
60) [16661, 5373, 6013525] C3 x C255 ---) [4909, 9193, 3748725] C255
61) [16673, 6247, 5217028] C3 x C255 ---) [4513, 7395, 266768] C255
62) [17053, 5898, 442949] C3 x C255 ---) [2621, 2949, 2063413] C255
63) [17333, 4510, 647777] C3 x C255 21) [3833, 2255, 1109312] C3 x C255
64) [17417, 1015, 218368] C3 x C255 ---) [853, 2030, 156753] C255
65) [18233, 9483, 22477264] C3 x C255 30) [4861, 7089, 11395625] C3 x C255
66) [18661, 4789, 1250325] C3 x C255 ---) [5557, 9578, 17933221] C255
67) [21737, 479, 8452] C3 x C255 ---) [2113, 958, 195633] C255
68) [27673, 1442, 409149] C3 x C255 ---) [269, 721, 27673] C255
69) [29569, 1098, 183125] C3 x C255 ---) [293, 549, 29569] C255
70) [37537, 826, 20421] C3 x C255 ---) [2269, 413, 37537] C255
71) [47417, 227, 1028] C3 x C255 ---) [257, 454, 47417] C3 x C3 x C255
72) [90989, 417, 20725] C3 x C255 ---) [829, 834, 90989] C255
73) [91253, 725, 108593] C3 x C255 ---) [113, 1450, 91253] C255
74) [91837, 361, 9621] C3 x C255 ---) [1069, 722, 91837] C255
75) [113417, 355, 3152] C3 x C255 ---) [197, 710, 113417] C255
76) [235069, 633, 41405] C3 x C255 ---) [5, 989, 235069] C51
77) [403301, 637, 617] C3 x C255 6) [617, 1274, 403301] C3 x C255
78) [441281, 893, 89042] C3 x C255 ---) [8, 1786, 441281] C255
79) [493393, 727, 8784] C3 x C255 ---) [61, 1454, 493393] C255
80) [531457, 733, 1458] C3 x C255 ---) [8, 1466, 531457] C255
81) [607337, 2195, 1052672] C3 x C255 5) [257, 4390, 607337] C3 x C255
82) [812057, 915, 6292] C3 x C255 ---) [13, 1830, 812057] C255
83) [817897, 1843, 644688] C3 x C255 ---) [37, 3686, 817897] C255
84) [952829, 977, 425] C3 x C255 ---) [17, 1954, 952829] C255
85) [1014749, 1057, 25625] C3 x C255 ---) [41, 2114, 1014749] C255
86) [1246601, 1699, 410000] C3 x C255 ---) [41, 3398, 1246601] C255
87) [1326049, 1581, 293378] C3 x C255 ---) [8, 3162, 1326049] C255
88) [1545001, 1291, 30420] C3 x C255 ---) [5, 2582, 1545001] C255
89) [2303849, 1907, 333200] C3 x C255 ---) [17, 3814, 2303849] C3 x C51
90) [3138929, 2023, 238400] C3 x C255 1) [149, 4046, 3138929] C3 x C255
91) [4286209, 2527, 524880] C3 x C255 ---) [5, 4341, 4286209] C255
92) [4795337, 3235, 1417472] C3 x C255 ---) [113, 6470, 4795337] C255
93) [6600449, 2687, 154880] C3 x C255 ---) [5, 5374, 6600449] C255
94) [7847641, 2971, 244800] C3 x C255 ---) [17, 5942, 7847641] C255
95) [9948313, 3259, 168192] C3 x C255 ---) [73, 6518, 9948313] C255
96) [13848617, 4403, 1384448] C3 x C255 ---) [8, 8806, 13848617] C255
97) [15846713, 4075, 189728] C3 x C255 ---) [8, 8150, 15846713] C255