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 number 3 non-normal (D4) quartic CM field invariants: 134 fields

K Quartic invariants Cl(OK) Igusa invariants Kr Reflex invariants Cl(OKr) Igusa invariants
1) [5, 101, 2549] C3 ■ 132) [2549, 77, 845] C3 ■
2) [5, 37, 281] C3 ■ 84) [281, 19, 20] C3 ■
3) [5, 101, 2269] C3 ■ 129) [2269, 57, 245] C3 ■
4) [5, 106, 2789] C3 ■ 133) [2789, 53, 5] C3 ■
5) [5, 41, 409] C3 ■ 93) [409, 27, 80] C3 ■
6) [5, 57, 661] C3 ■ 101) [661, 29, 45] C3 ■
7) [5, 33, 241] C3 ■ 81) [241, 31, 180] C3 ■
8) [5, 97, 1901] C3 ■ ---) [1901, 49, 125] C3 x C3 ■
9) [5, 49, 569] C3 ■ 97) [569, 43, 320] C3 ■
10) [5, 46, 449] C3 ■ 95) [449, 23, 20] C3 ■
11) [5, 53, 701] C3 ■ 103) [701, 41, 245] C3 ■
12) [5, 61, 929] C3 ■ 109) [929, 47, 320] C3 ■
13) [5, 106, 2309] C3 ■ 130) [2309, 53, 125] C3 ■
14) [5, 81, 1429] C3 ■ ---) [1429, 77, 1125] C15 ■
15) [5, 61, 829] C3 ■ 107) [829, 57, 605] C3 ■
16) [5, 42, 421] C3 ■ 94) [421, 21, 5] C3 ■
17) [5, 58, 821] C3 ■ 106) [821, 29, 5] C3 ■
18) [5, 66, 1069] C3 ■ 113) [1069, 33, 5] C3 ■
19) [5, 73, 1181] C3 ■ 117) [1181, 41, 125] C3 ■
20) [5, 89, 1949] C3 ■ 128) [1949, 73, 845] C3 ■
21) [8, 26, 97] C3 ■ 69) [97, 13, 18] C3 ■
22) [8, 70, 1097] C3 ■ 114) [1097, 35, 32] C3 ■
23) [8, 86, 1049] C3 ■ 112) [1049, 43, 200] C3 ■
24) [8, 98, 1433] C3 ■ 121) [1433, 49, 242] C3 ■
25) [8, 50, 617] C3 ■ 100) [617, 25, 2] C3 ■
26) [8, 82, 1033] C3 ■ 111) [1033, 41, 162] C3 ■
27) [8, 118, 2969] C3 ■ 134) [2969, 59, 128] C3 ■
28) [8, 86, 1721] C3 ■ 125) [1721, 43, 32] C3 ■
29) [8, 82, 1481] C3 ■ 123) [1481, 41, 50] C3 ■
30) [8, 70, 937] C3 ■ 110) [937, 35, 72] C3 ■
31) [8, 70, 1193] C3 ■ 118) [1193, 35, 8] C3 ■
32) [8, 114, 2857] C3 ■ ---) [2857, 57, 98] C3 x C3 ■
33) [8, 98, 2393] C3 ■ 131) [2393, 49, 2] C3 ■
34) [8, 54, 601] C3 ■ 98) [601, 27, 32] C3 ■
35) [13, 33, 113] C3 ■ 76) [113, 35, 52] C3 ■
36) [13, 101, 1117] C3 ■ 115) [1117, 73, 1053] C3 ■
37) [13, 77, 1453] C3 ■ 122) [1453, 125, 637] C3 ■
38) [13, 53, 673] C3 ■ 102) [673, 83, 208] C3 ■
39) [13, 42, 389] C3 ■ 92) [389, 21, 13] C3 ■
40) [13, 33, 269] C3 ■ 83) [269, 61, 325] C3 ■
41) [13, 98, 1933] C3 ■ 127) [1933, 49, 117] C3 ■
42) [17, 175, 7652] C3 ■ 126) [1913, 139, 4352] C3 ■
43) [17, 167, 6628] C3 ■ 124) [1657, 107, 2448] C3 ■
44) [17, 111, 3076] C3 ■ 105) [769, 87, 1700] C3 ■
45) [17, 26, 101] C3 ■ 71) [101, 13, 17] C3 ■
46) [17, 86, 761] C3 ■ ---) [761, 43, 272] C3 x C3 ■
47) [17, 103, 2308] C3 ■ ---) [577, 55, 612] C21 ■
48) [17, 78, 1249] C3 ■ 119) [1249, 39, 68] C3 ■
49) [29, 34, 173] C3 ■ 78) [173, 17, 29] C3 ■
50) [29, 65, 701] C3 ■ 104) [701, 130, 1421] C3 ■
51) [29, 89, 349] C3 ■ 89) [349, 57, 725] C3 ■
52) [37, 137, 613] C3 ■ 99) [613, 113, 1813] C3 ■
53) [37, 41, 337] C3 ■ 86) [337, 82, 333] C3 ■
54) [37, 45, 53] C3 ■ 64) [53, 25, 37] C3 ■
55) [37, 33, 41] C3 ■ 59) [41, 31, 148] C3 ■
56) [37, 77, 733] C3 ■ ---) [733, 154, 2997] C3 x C3 ■
57) [37, 202, 10053] C3 ■ 116) [1117, 101, 37] C3 ■
58) [37, 21, 101] C3 ■ 72) [101, 42, 37] C3 ■
59) [41, 31, 148] C3 ■ 55) [37, 33, 41] C3 ■
60) [41, 118, 857] C3 ■ 108) [857, 59, 656] C3 ■
61) [41, 111, 1348] C3 ■ 87) [337, 79, 1476] C3 ■
62) [41, 151, 5444] C3 ■ 120) [1361, 211, 2624] C3 ■
63) [41, 103, 1412] C3 ■ 90) [353, 107, 656] C3 ■
64) [53, 25, 37] C3 ■ 54) [37, 45, 53] C3 ■
65) [61, 29, 73] C3 ■ 66) [73, 58, 549] C3 ■
66) [73, 58, 549] C3 ■ 65) [61, 29, 73] C3 ■
67) [73, 78, 353] C3 ■ 91) [353, 39, 292] C3 ■
68) [89, 78, 97] C3 ■ 70) [97, 39, 356] C3 ■
69) [97, 13, 18] C3 ■ 21) [8, 26, 97] C3 ■
70) [97, 39, 356] C3 ■ 68) [89, 78, 97] C3 ■
71) [101, 13, 17] C3 ■ 45) [17, 26, 101] C3 ■
72) [101, 42, 37] C3 ■ 58) [37, 21, 101] C3 ■
73) [109, 161, 349] C3 ■ 88) [349, 145, 981] C3 ■
74) [113, 119, 1252] C3 ■ 85) [313, 171, 7232] C3 ■
75) [113, 94, 401] C3 ■ ---) [401, 47, 452] C15 ■
76) [113, 35, 52] C3 ■ 35) [13, 33, 113] C3 ■
77) [137, 103, 1796] C3 ■ 96) [449, 206, 3425] C3 ■
78) [173, 17, 29] C3 ■ 49) [29, 34, 173] C3 ■
79) [193, 131, 3856] C3 ■ 80) [241, 199, 6948] C3 ■
80) [241, 199, 6948] C3 ■ 79) [193, 131, 3856] C3 ■
81) [241, 31, 180] C3 ■ 7) [5, 33, 241] C3 ■
82) [257, 23, 68] C3 ■ ---) [17, 46, 257] C1 ■
83) [269, 61, 325] C3 ■ 40) [13, 33, 269] C3 ■
84) [281, 19, 20] C3 ■ 2) [5, 37, 281] C3 ■
85) [313, 171, 7232] C3 ■ 74) [113, 119, 1252] C3 ■
86) [337, 82, 333] C3 ■ 53) [37, 41, 337] C3 ■
87) [337, 79, 1476] C3 ■ 61) [41, 111, 1348] C3 ■
88) [349, 145, 981] C3 ■ 73) [109, 161, 349] C3 ■
89) [349, 57, 725] C3 ■ 51) [29, 89, 349] C3 ■
90) [353, 107, 656] C3 ■ 63) [41, 103, 1412] C3 ■
91) [353, 39, 292] C3 ■ 67) [73, 78, 353] C3 ■
92) [389, 21, 13] C3 ■ 39) [13, 42, 389] C3 ■
93) [409, 27, 80] C3 ■ 5) [5, 41, 409] C3 ■
94) [421, 21, 5] C3 ■ 16) [5, 42, 421] C3 ■
95) [449, 23, 20] C3 ■ 10) [5, 46, 449] C3 ■
96) [449, 206, 3425] C3 ■ 77) [137, 103, 1796] C3 ■
97) [569, 43, 320] C3 ■ 9) [5, 49, 569] C3 ■
98) [601, 27, 32] C3 ■ 34) [8, 54, 601] C3 ■
99) [613, 113, 1813] C3 ■ 52) [37, 137, 613] C3 ■
100) [617, 25, 2] C3 ■ 25) [8, 50, 617] C3 ■
101) [661, 29, 45] C3 ■ 6) [5, 57, 661] C3 ■
102) [673, 83, 208] C3 ■ 38) [13, 53, 673] C3 ■
103) [701, 41, 245] C3 ■ 11) [5, 53, 701] C3 ■
104) [701, 130, 1421] C3 ■ 50) [29, 65, 701] C3 ■
105) [769, 87, 1700] C3 ■ 44) [17, 111, 3076] C3 ■
106) [821, 29, 5] C3 ■ 17) [5, 58, 821] C3 ■
107) [829, 57, 605] C3 ■ 15) [5, 61, 829] C3 ■
108) [857, 59, 656] C3 ■ 60) [41, 118, 857] C3 ■
109) [929, 47, 320] C3 ■ 12) [5, 61, 929] C3 ■
110) [937, 35, 72] C3 ■ 30) [8, 70, 937] C3 ■
111) [1033, 41, 162] C3 ■ 26) [8, 82, 1033] C3 ■
112) [1049, 43, 200] C3 ■ 23) [8, 86, 1049] C3 ■
113) [1069, 33, 5] C3 ■ 18) [5, 66, 1069] C3 ■
114) [1097, 35, 32] C3 ■ 22) [8, 70, 1097] C3 ■
115) [1117, 73, 1053] C3 ■ 36) [13, 101, 1117] C3 ■
116) [1117, 101, 37] C3 ■ 57) [37, 202, 10053] C3 ■
117) [1181, 41, 125] C3 ■ 19) [5, 73, 1181] C3 ■
118) [1193, 35, 8] C3 ■ 31) [8, 70, 1193] C3 ■
119) [1249, 39, 68] C3 ■ 48) [17, 78, 1249] C3 ■
120) [1361, 211, 2624] C3 ■ 62) [41, 151, 5444] C3 ■
121) [1433, 49, 242] C3 ■ 24) [8, 98, 1433] C3 ■
122) [1453, 125, 637] C3 ■ 37) [13, 77, 1453] C3 ■
123) [1481, 41, 50] C3 ■ 29) [8, 82, 1481] C3 ■
124) [1657, 107, 2448] C3 ■ 43) [17, 167, 6628] C3 ■
125) [1721, 43, 32] C3 ■ 28) [8, 86, 1721] C3 ■
126) [1913, 139, 4352] C3 ■ 42) [17, 175, 7652] C3 ■
127) [1933, 49, 117] C3 ■ 41) [13, 98, 1933] C3 ■
128) [1949, 73, 845] C3 ■ 20) [5, 89, 1949] C3 ■
129) [2269, 57, 245] C3 ■ 3) [5, 101, 2269] C3 ■
130) [2309, 53, 125] C3 ■ 13) [5, 106, 2309] C3 ■
131) [2393, 49, 2] C3 ■ 33) [8, 98, 2393] C3 ■
132) [2549, 77, 845] C3 ■ 1) [5, 101, 2549] C3 ■
133) [2789, 53, 5] C3 ■ 4) [5, 106, 2789] C3 ■
134) [2969, 59, 128] C3 ■ 27) [8, 118, 2969] C3 ■