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 C273 non-normal (D4) quartic CM field invariants: 90 fields

K Quartic invariants Cl(OK) Igusa invariants Kr Reflex invariants Cl(OKr) Igusa invariants
1) [5, 10366, 26853809] C3 x C273 90) [26853809, 5183, 2420] C3 x C273
2) [13, 4681, 1955977] C3 x C273 78) [1955977, 2723, 1364688] C3 x C273
3) [229, 834, 172973] C3 x C273 ---) [172973, 417, 229] C273
4) [229, 2366, 212353] C3 x C273 ---) [212353, 1183, 296784] C273
5) [229, 825, 160481] C3 x C273 ---) [160481, 1650, 38701] C273
6) [257, 642, 102013] C3 x C273 ---) [102013, 321, 257] C273
7) [257, 730, 123973] C3 x C273 ---) [123973, 365, 2313] C273
8) [701, 893, 194981] C3 x C273 72) [194981, 1786, 17525] C3 x C273
9) [733, 1082, 266293] C3 x C273 ---) [266293, 541, 6597] C273
10) [1229, 985, 80021] C3 x C273 ---) [80021, 1970, 650141] C273
11) [1373, 313, 7673] C3 x C273 35) [7673, 626, 67277] C3 x C273
12) [1489, 1259, 124900] C3 x C273 ---) [1249, 779, 148900] C273
13) [2089, 915, 208784] C3 x C273 ---) [13049, 1830, 2089] C7 x C273
14) [2089, 1199, 129088] C3 x C273 ---) [2017, 1763, 409444] C273
15) [2557, 3382, 2695833] C3 x C273 ---) [6113, 1691, 40912] C1365
16) [2713, 5386, 1511541] C3 x C273 61) [18661, 2693, 1435177] C3 x C273
17) [2713, 1546, 65781] C3 x C273 ---) [7309, 773, 132937] C273
18) [2777, 266, 6581] C3 x C273 ---) [6581, 133, 2777] C273
19) [3221, 877, 127057] C3 x C273 ---) [2593, 1754, 260901] C273
20) [3221, 989, 11813] C3 x C273 ---) [11813, 1978, 930869] C273
21) [3877, 2850, 1270733] C3 x C273 ---) [4397, 1425, 189973] C273
22) [4481, 1215, 367936] C3 x C273 ---) [5749, 2430, 4481] C273
23) [4493, 241, 13397] C3 x C273 ---) [13397, 482, 4493] C273
24) [4493, 322, 7949] C3 x C273 ---) [7949, 161, 4493] C273
25) [4649, 6214, 6975625] C3 x C273 ---) [11161, 3107, 669456] C273
26) [4933, 2397, 665621] C3 x C273 ---) [5501, 4794, 3083125] C273
27) [5197, 5710, 1415713] C3 x C273 37) [8377, 2855, 1683828] C3 x C273
28) [5281, 1343, 153856] C3 x C273 ---) [601, 1247, 84496] C273
29) [5297, 306, 2221] C3 x C273 ---) [2221, 153, 5297] C273
30) [5477, 213, 9973] C3 x C273 ---) [9973, 426, 5477] C273
31) [5477, 5469, 7410397] C3 x C273 ---) [5413, 4885, 5964453] C273
32) [6637, 3581, 2925477] C3 x C273 ---) [4013, 4041, 2395957] C273
33) [7057, 695, 34308] C3 x C273 ---) [953, 1390, 345793] C39
34) [7481, 1494, 79225] C3 x C273 ---) [3169, 747, 119696] C273
35) [7673, 626, 67277] C3 x C273 11) [1373, 313, 7673] C3 x C273
36) [7673, 4571, 1998932] C3 x C273 ---) [2957, 3061, 2217497] C273
37) [8377, 2855, 1683828] C3 x C273 27) [5197, 5710, 1415713] C3 x C273
38) [8581, 2597, 1512337] C3 x C273 ---) [5233, 5194, 695061] C273
39) [8837, 394, 3461] C3 x C273 ---) [3461, 197, 8837] C273
40) [9281, 5131, 64208] C3 x C273 ---) [4013, 5669, 1123001] C273
41) [9749, 4394, 4787813] C3 x C273 ---) [5693, 2197, 9749] C273
42) [10301, 3169, 35825] C3 x C273 ---) [1433, 3403, 659264] C273
43) [10301, 5450, 4088101] C3 x C273 ---) [4861, 2725, 834381] C273
44) [10949, 5317, 1021037] C3 x C273 ---) [3533, 5413, 10949] C273
45) [11057, 643, 34256] C3 x C273 ---) [2141, 1286, 276425] C273
46) [12197, 3710, 318593] C3 x C273 ---) [2633, 1855, 780608] C273
47) [12401, 1819, 749684] C3 x C273 ---) [1109, 3638, 310025] C273
48) [12401, 5202, 6715597] C3 x C273 ---) [2797, 2601, 12401] C273
49) [12821, 1837, 840437] C3 x C273 ---) [4973, 3674, 12821] C273
50) [13877, 3146, 1974757] C3 x C273 ---) [3733, 1573, 124893] C273
51) [13877, 5938, 2098493] C3 x C273 ---) [5813, 2969, 1679117] C273
52) [15349, 1078, 44937] C3 x C273 ---) [4993, 539, 61396] C273
53) [15737, 3851, 3703616] C3 x C273 ---) [1181, 3233, 1904177] C273
54) [15773, 2889, 601] C3 x C273 ---) [601, 1759, 567828] C273
55) [15773, 2594, 104909] C3 x C273 ---) [2141, 1297, 394325] C273
56) [16661, 7769, 6654709] C3 x C273 ---) [4861, 9045, 6014621] C273
57) [17257, 5662, 1111761] C3 x C273 ---) [2521, 2831, 1725700] C3 x C39
58) [18097, 4255, 178452] C3 x C273 ---) [4957, 8510, 17391217] C273
59) [18269, 1621, 104273] C3 x C273 ---) [617, 3242, 2210549] C273
60) [18521, 3063, 673972] C3 x C273 ---) [997, 3837, 3130049] C273
61) [18661, 2693, 1435177] C3 x C273 16) [2713, 5386, 1511541] C3 x C273
62) [18661, 658, 33597] C3 x C273 ---) [3733, 329, 18661] C273
63) [23297, 2179, 1134592] C3 x C273 ---) [277, 1545, 23297] C273
64) [34877, 193, 593] C3 x C273 ---) [593, 386, 34877] C273
65) [35393, 987, 22336] C3 x C273 ---) [349, 1974, 884825] C273
66) [44621, 850, 2141] C3 x C273 ---) [2141, 425, 44621] C273
67) [69761, 319, 8000] C3 x C273 ---) [5, 557, 69761] C39
68) [81373, 313, 4149] C3 x C273 ---) [461, 626, 81373] C273
69) [99257, 1410, 99997] C3 x C273 ---) [277, 705, 99257] C273
70) [122273, 1139, 49216] C3 x C273 ---) [769, 2278, 1100457] C273
71) [177481, 1714, 24525] C3 x C273 ---) [109, 857, 177481] C273
72) [194981, 1786, 17525] C3 x C273 8) [701, 893, 194981] C3 x C273
73) [254437, 2194, 185661] C3 x C273 ---) [421, 1097, 254437] C273
74) [1203913, 1187, 51264] C3 x C273 ---) [89, 2374, 1203913] C273
75) [1281257, 3431, 60112] C3 x C273 ---) [13, 2865, 1281257] C273
76) [1825297, 1399, 32976] C3 x C273 ---) [229, 2798, 1825297] C3 x C3 x C273
77) [1828601, 1355, 1856] C3 x C273 ---) [29, 2710, 1828601] C273
78) [1955977, 2723, 1364688] C3 x C273 2) [13, 4681, 1955977] C3 x C273
79) [2347129, 1547, 11520] C3 x C273 ---) [5, 3094, 2347129] C273
80) [2827553, 2285, 598418] C3 x C273 ---) [8, 4570, 2827553] C273
81) [3390169, 1843, 1620] C3 x C273 ---) [5, 3686, 3390169] C273
82) [3732761, 1937, 4802] C3 x C273 ---) [8, 3874, 3732761] C273
83) [4246057, 2483, 479808] C3 x C273 ---) [17, 4966, 4246057] C273
84) [4292809, 2083, 11520] C3 x C273 ---) [5, 4166, 4292809] C273
85) [6095329, 3343, 1270080] C3 x C273 ---) [5, 4989, 6095329] C273
86) [7005529, 3547, 1393920] C3 x C273 ---) [5, 5361, 7005529] C273
87) [8963753, 2995, 1568] C3 x C273 ---) [8, 5990, 8963753] C273
88) [9617369, 3163, 96800] C3 x C273 ---) [8, 6326, 9617369] C273
89) [10970489, 3467, 262400] C3 x C273 ---) [41, 6934, 10970489] C273
90) [26853809, 5183, 2420] C3 x C273 1) [5, 10366, 26853809] C3 x C273