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 C18 x C18 non-normal (D4) quartic CM field invariants: 89 fields

K Quartic invariants Cl(OK) Igusa invariants Kr Reflex invariants Cl(OKr) Igusa invariants
1) [5, 6745, 9729245] C18 x C18 ---) [9729245, 3625, 852845] C18 x C504
2) [5, 1644, 657684] C18 x C18 ---) [18269, 822, 4500] C3 x C18 x C18
3) [5, 3273, 2630601] C18 x C18 ---) [292289, 2211, 564480] C18 x C72
4) [5, 1088, 295916] C18 x C18 ---) [295916, 544, 5] C18 x C36
5) [5, 1360, 447820] C18 x C18 ---) [447820, 680, 3645] C3 x C18 x C180
6) [5, 5222, 5813801] C18 x C18 81) [118649, 2611, 250880] C18 x C18
7) [12, 2354, 856129] C18 x C18 ---) [856129, 1177, 132300] C9 x C36
8) [13, 6670, 5111025] C18 x C18 ---) [204441, 3335, 1502800] C18 x C90
9) [13, 776, 126507] C18 x C18 ---) [506028, 1552, 96148] C18 x C72
10) [13, 6142, 3419841] C18 x C18 ---) [3419841, 3071, 1502800] C18 x C36
11) [24, 788, 75886] C18 x C18 ---) [303544, 1180, 272214] C18 x C36
12) [24, 4870, 4256521] C18 x C18 ---) [4256521, 2435, 418176] C9 x C36
13) [28, 496, 8521] C18 x C18 60) [8521, 314, 16128] C18 x C18
14) [28, 8486, 15680617] C18 x C18 ---) [15680617, 4243, 580608] C9 x C36
15) [28, 7526, 13756969] C18 x C18 ---) [13756969, 3763, 100800] C2 x C18 x C18
16) [37, 767, 146619] C18 x C18 ---) [65164, 1534, 1813] C2 x C18 x C18
17) [56, 7174, 3906569] C18 x C18 ---) [3906569, 3587, 2240000] C18 x C2016
18) [76, 822, 141485] C18 x C18 ---) [141485, 411, 6859] C6 x C18 x C18
19) [93, 6486, 5160249] C18 x C18 ---) [573361, 3243, 1339200] C9 x C36
20) [109, 1214, 270349] C18 x C18 ---) [270349, 607, 24525] C2 x C18 x C18
21) [157, 207, 9731] C18 x C18 ---) [38924, 414, 3925] C18 x C180
22) [172, 234, 13646] C18 x C18 ---) [54584, 468, 172] C9 x C36
23) [181, 1318, 431385] C18 x C18 ---) [431385, 659, 724] C18 x C36
24) [213, 344, 28732] C18 x C18 ---) [28732, 172, 213] C18 x C36
25) [268, 614, 86142] C18 x C18 ---) [7032, 426, 29547] C3 x C18 x C36
26) [301, 445, 49431] C18 x C18 ---) [197724, 890, 301] C18 x C36
27) [413, 1406, 71297] C18 x C18 ---) [71297, 703, 105728] C9 x C36
28) [449, 643, 78106] C18 x C18 ---) [6376, 1286, 101025] C18 x C36
29) [501, 758, 71497] C18 x C18 ---) [71497, 379, 18036] C18 x C36
30) [764, 2326, 982793] C18 x C18 ---) [20057, 1163, 92444] C9 x C180
31) [956, 180, 7144] C18 x C18 ---) [7144, 90, 239] C18 x C36
32) [1049, 878, 188525] C18 x C18 ---) [7541, 439, 1049] C9 x C36
33) [1081, 322, 21597] C18 x C18 ---) [21597, 161, 1081] C3 x C18 x C36
34) [1129, 735, 132516] C18 x C18 ---) [409, 1470, 10161] C2 x C18
35) [1129, 806, 90153] C18 x C18 ---) [1113, 403, 18064] C2 x C36
36) [1129, 322, 7857] C18 x C18 ---) [97, 161, 4516] C2 x C18
37) [1129, 711, 1908] C18 x C18 ---) [53, 501, 10161] C36
38) [1129, 187, 8460] C18 x C18 ---) [940, 374, 1129] C6 x C36
39) [1529, 505, 17504] C18 x C18 48) [4376, 1010, 185009] C18 x C18
40) [1569, 306, 17133] C18 x C18 ---) [17133, 153, 1569] C9 x C36
41) [1676, 556, 6473] C18 x C18 54) [6473, 1112, 283244] C18 x C18
42) [1912, 3850, 1747737] C18 x C18 67) [21577, 1925, 489472] C18 x C18
43) [2281, 1965, 6716] C18 x C18 ---) [6716, 3930, 3834361] C18 x C72
44) [2456, 780, 48334] C18 x C18 ---) [1144, 660, 74294] C18 x C36
45) [3004, 242, 11637] C18 x C18 ---) [1293, 121, 751] C9 x C36
46) [3137, 227, 5824] C18 x C18 ---) [364, 454, 28233] C2 x C2 x C18
47) [3137, 71, 476] C18 x C18 ---) [476, 142, 3137] C2 x C2 x C18
48) [4376, 1010, 185009] C18 x C18 39) [1529, 505, 17504] C18 x C18
49) [4409, 225, 2736] C18 x C18 ---) [76, 450, 39681] C2 x C18
50) [4409, 627, 9000] C18 x C18 ---) [40, 1254, 357129] C2 x C36
51) [5189, 1146, 141525] C18 x C18 ---) [629, 573, 46701] C2 x C18 x C18
52) [5521, 379, 1404] C18 x C18 ---) [156, 758, 138025] C2 x C36
53) [5521, 280, 14079] C18 x C18 ---) [156, 560, 22084] C2 x C36
54) [6473, 1112, 283244] C18 x C18 41) [1676, 556, 6473] C18 x C18
55) [6809, 341, 13750] C18 x C18 ---) [88, 682, 61281] C36
56) [7697, 1964, 587171] C18 x C18 ---) [2444, 3928, 1508612] C2 x C18 x C18
57) [7873, 97, 384] C18 x C18 ---) [24, 194, 7873] C2 x C18
58) [8117, 1255, 50813] C18 x C18 ---) [1037, 2510, 1371773] C2 x C18 x C18
59) [8261, 264, 9163] C18 x C18 ---) [748, 528, 33044] C18 x C36
60) [8521, 314, 16128] C18 x C18 13) [28, 496, 8521] C18 x C18
61) [10433, 2571, 502272] C18 x C18 ---) [872, 5142, 4600953] C2 x C18 x C18
62) [10588, 654, 11637] C18 x C18 ---) [1293, 327, 23823] C9 x C36
63) [10721, 363, 8820] C18 x C18 ---) [5, 669, 96489] C2 x C18
64) [12409, 117, 320] C18 x C18 ---) [5, 234, 12409] C36
65) [16537, 586, 19701] C18 x C18 ---) [2189, 293, 16537] C9 x C36
66) [19441, 1192, 335775] C18 x C18 ---) [444, 2384, 77764] C2 x C36
67) [21577, 1925, 489472] C18 x C18 42) [1912, 3850, 1747737] C18 x C18
68) [21628, 298, 573] C18 x C18 ---) [573, 149, 5407] C9 x C36
69) [21701, 201, 4675] C18 x C18 ---) [748, 402, 21701] C2 x C18 x C18
70) [35873, 207, 1744] C18 x C18 ---) [109, 414, 35873] C9 x C18
71) [38821, 209, 1215] C18 x C18 ---) [60, 418, 38821] C18 x C36
72) [44236, 828, 127160] C18 x C18 ---) [440, 414, 11059] C18 x C36
73) [56089, 283, 6000] C18 x C18 ---) [60, 566, 56089] C2 x C2 x C18
74) [75596, 3262, 2584565] C18 x C18 ---) [485, 1631, 18899] C2 x C18 x C18
75) [84121, 602, 6480] C18 x C18 ---) [5, 1204, 336484] C9 x C36
76) [89761, 2191, 100548] C18 x C18 ---) [57, 1199, 359044] C36
77) [92741, 1346, 81965] C18 x C18 ---) [485, 673, 92741] C2 x C18 x C18
78) [97469, 313, 125] C18 x C18 ---) [5, 626, 97469] C18
79) [101933, 1322, 29189] C18 x C18 ---) [101, 661, 101933] C9 x C18
80) [115657, 1741, 34914] C18 x C18 ---) [264, 3482, 2891425] C18 x C36
81) [118649, 2611, 250880] C18 x C18 6) [5, 5222, 5813801] C18 x C18
82) [151673, 523, 30464] C18 x C18 ---) [476, 1046, 151673] C18 x C36
83) [153481, 2319, 999108] C18 x C18 ---) [33, 1583, 613924] C36
84) [244289, 927, 153760] C18 x C18 ---) [40, 1854, 244289] C2 x C18 x C18
85) [287409, 537, 240] C18 x C18 ---) [60, 1074, 287409] C18 x C36
86) [350401, 1951, 864000] C18 x C18 ---) [60, 3902, 350401] C2 x C18 x C18
87) [986521, 1339, 201600] C18 x C18 ---) [56, 2678, 986521] C9 x C36
88) [1040641, 4330, 524661] C18 x C18 ---) [141, 2165, 1040641] C9 x C36
89) [3416233, 2035, 181248] C18 x C18 ---) [177, 4070, 3416233] C9 x C36