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 C969 non-normal (D4) quartic CM field invariants: 143 fields

K Quartic invariants Cl(OK) Igusa invariants Kr Reflex invariants Cl(OKr) Igusa invariants
1) [8, 5870, 8609617] C969 139) [8609617, 2935, 1152] C969
2) [17, 3326, 2085569] C969 126) [2085569, 1663, 170000] C969
3) [17, 3422, 2247521] C969 128) [2247521, 1711, 170000] C969
4) [37, 3198, 2518913] C969 129) [2518913, 1599, 9472] C969
5) [37, 4734, 5451137] C969 134) [5451137, 2367, 37888] C969
6) [97, 1951, 652816] C969 101) [40801, 1199, 349200] C969
7) [101, 4366, 4351793] C969 133) [4351793, 2183, 103424] C969
8) [101, 3422, 2824097] C969 130) [2824097, 1711, 25856] C969
9) [173, 3662, 1182449] C969 ---) [1182449, 1831, 542528] C3 x C969
10) [173, 3182, 1822673] C969 125) [1822673, 1591, 177152] C969
11) [181, 3510, 1678361] C969 123) [1678361, 1755, 350416] C969
12) [193, 3982, 3951729] C969 112) [439081, 1991, 3088] C969
13) [197, 2878, 1049473] C969 117) [1049473, 1439, 255312] C969
14) [257, 943, 217108] C969 ---) [54277, 1886, 20817] C323
15) [269, 2462, 671777] C969 116) [671777, 1231, 210896] C969
16) [313, 571, 75172] C969 96) [18793, 1142, 25353] C969
17) [313, 1907, 420804] C969 72) [11689, 1067, 281700] C969
18) [337, 4038, 3537161] C969 132) [3537161, 2019, 134800] C969
19) [373, 2166, 1149017] C969 ---) [1149017, 1083, 5968] C4845
20) [433, 1171, 61252] C969 79) [15313, 2342, 1126233] C969
21) [461, 2774, 1186169] C969 120) [1186169, 1387, 184400] C969
22) [857, 2823, 218128] C969 76) [13633, 2111, 1110672] C969
23) [1289, 922, 83621] C969 104) [83621, 461, 32225] C969
24) [1409, 1763, 621700] C969 61) [6217, 2903, 202896] C969
25) [2089, 2754, 885053] C969 ---) [5237, 1377, 252769] C323
26) [2213, 1565, 9817] C969 ---) [9817, 3130, 2409957] C323
27) [2273, 1807, 270224] C969 86) [16889, 3614, 2184353] C969
28) [2617, 1363, 275364] C969 64) [7649, 2726, 756313] C969
29) [2857, 2047, 446868] C969 ---) [12413, 4094, 2402737] C323
30) [2857, 907, 204948] C969 ---) [5693, 1814, 2857] C323
31) [2857, 5202, 6205229] C969 ---) [17189, 2601, 139993] C323
32) [2897, 4663, 2375936] C969 ---) [9281, 3571, 11588] C3 x C969
33) [3209, 4907, 756100] C969 63) [7561, 2691, 628964] C969
34) [3229, 1641, 439925] C969 ---) [17597, 3282, 933181] C323
35) [3313, 2175, 744512] C969 71) [11633, 4350, 1752577] C969
36) [3433, 1427, 467028] C969 75) [12973, 2854, 168217] C969
37) [3593, 1459, 56996] C969 77) [14249, 2918, 1900697] C969
38) [3833, 7747, 4439296] C969 87) [17341, 4593, 1107737] C969
39) [4021, 6437, 1286361] C969 ---) [15881, 6023, 1029376] C3 x C969
40) [4049, 3211, 1839700] C969 93) [18397, 6422, 2951721] C969
41) [4057, 1354, 312277] C969 62) [6373, 677, 36513] C969
42) [4093, 6161, 9488457] C969 ---) [8713, 3247, 1047808] C3 x C969
43) [4153, 8123, 10016064] C969 88) [17389, 6653, 3027537] C969
44) [4261, 7125, 1390169] C969 70) [11489, 3591, 1704400] C969
45) [4421, 4958, 415825] C969 84) [16633, 2479, 1432404] C969
46) [4481, 3211, 2083600] C969 ---) [5209, 5107, 2581056] C323
47) [4909, 1353, 456425] C969 ---) [18257, 2706, 4909] C3 x C969
48) [4933, 5930, 7824357] C969 66) [10733, 2965, 241717] C969
49) [4957, 7153, 1607121] C969 98) [19841, 8251, 13403728] C969
50) [5077, 4730, 5572917] C969 73) [12637, 2365, 5077] C969
51) [5101, 8246, 3206025] C969 78) [14249, 4123, 3448276] C969
52) [5261, 4733, 2179357] C969 ---) [6037, 5001, 636581] C323
53) [5297, 255, 14932] C969 ---) [3733, 510, 5297] C323
54) [5381, 6505, 2602769] C969 80) [15401, 7711, 538100] C969
55) [5381, 7473, 13927801] C969 83) [16561, 6871, 4842900] C969
56) [5381, 237, 12697] C969 74) [12697, 474, 5381] C969
57) [5653, 654, 16481] C969 ---) [16481, 327, 22612] C3 x C969
58) [5749, 8074, 6156133] C969 ---) [17053, 4037, 2535309] C3 x C969
59) [5869, 3841, 3616425] C969 81) [16073, 7682, 287581] C969
60) [5881, 11514, 938693] C969 97) [19157, 5757, 8051089] C969
61) [6217, 2903, 202896] C969 24) [1409, 1763, 621700] C969
62) [6373, 677, 36513] C969 41) [4057, 1354, 312277] C969
63) [7561, 2691, 628964] C969 33) [3209, 4907, 756100] C969
64) [7649, 2726, 756313] C969 28) [2617, 1363, 275364] C969
65) [8837, 853, 2953] C969 ---) [2953, 1706, 715797] C323
66) [10733, 2965, 241717] C969 48) [4933, 5930, 7824357] C969
67) [10889, 2667, 76816] C969 ---) [4801, 5334, 6805625] C323
68) [11197, 562, 34173] C969 ---) [3797, 281, 11197] C323
69) [11257, 203, 7488] C969 ---) [13, 361, 11257] C57
70) [11489, 3591, 1704400] C969 44) [4261, 7125, 1390169] C969
71) [11633, 4350, 1752577] C969 35) [3313, 2175, 744512] C969
72) [11689, 1067, 281700] C969 17) [313, 1907, 420804] C969
73) [12637, 2365, 5077] C969 50) [5077, 4730, 5572917] C969
74) [12697, 474, 5381] C969 56) [5381, 237, 12697] C969
75) [12973, 2854, 168217] C969 36) [3433, 1427, 467028] C969
76) [13633, 2111, 1110672] C969 22) [857, 2823, 218128] C969
77) [14249, 2918, 1900697] C969 37) [3593, 1459, 56996] C969
78) [14249, 4123, 3448276] C969 51) [5101, 8246, 3206025] C969
79) [15313, 2342, 1126233] C969 20) [433, 1171, 61252] C969
80) [15401, 7711, 538100] C969 54) [5381, 6505, 2602769] C969
81) [16073, 7682, 287581] C969 59) [5869, 3841, 3616425] C969
82) [16369, 6583, 10502500] C969 ---) [4201, 5635, 1047616] C323
83) [16561, 6871, 4842900] C969 55) [5381, 7473, 13927801] C969
84) [16633, 2479, 1432404] C969 45) [4421, 4958, 415825] C969
85) [16673, 2199, 4276] C969 ---) [1069, 4357, 3751425] C323
86) [16889, 3614, 2184353] C969 27) [2273, 1807, 270224] C969
87) [17341, 4593, 1107737] C969 38) [3833, 7747, 4439296] C969
88) [17389, 6653, 3027537] C969 43) [4153, 8123, 10016064] C969
89) [17609, 5510, 6463049] C969 ---) [4721, 2755, 281744] C323
90) [18097, 4467, 4441088] C969 ---) [4337, 8934, 2189737] C323
91) [18229, 658, 35325] C969 ---) [157, 329, 18229] C51
92) [18257, 3499, 2946644] C969 ---) [2549, 6998, 456425] C323
93) [18397, 6422, 2951721] C969 40) [4049, 3211, 1839700] C969
94) [18521, 751, 99328] C969 ---) [97, 1263, 296336] C323
95) [18701, 4981, 475409] C969 ---) [3929, 9775, 12641876] C323
96) [18793, 1142, 25353] C969 16) [313, 571, 75172] C969
97) [19157, 5757, 8051089] C969 60) [5881, 11514, 938693] C969
98) [19841, 8251, 13403728] C969 49) [4957, 7153, 1607121] C969
99) [30677, 205, 2837] C969 ---) [2837, 410, 30677] C323
100) [32353, 971, 162916] C969 ---) [241, 1942, 291177] C323
101) [40801, 1199, 349200] C969 6) [97, 1951, 652816] C969
102) [70313, 3671, 398336] C969 ---) [389, 5233, 3445337] C323
103) [79669, 285, 389] C969 ---) [389, 570, 79669] C323
104) [83621, 461, 32225] C969 23) [1289, 922, 83621] C969
105) [85517, 737, 114413] C969 ---) [677, 1474, 85517] C323
106) [100109, 1309, 203125] C969 ---) [13, 657, 100109] C51
107) [111593, 2363, 28928] C969 ---) [113, 2675, 1785488] C57
108) [152809, 723, 92480] C969 ---) [5, 809, 152809] C57
109) [267737, 587, 19208] C969 ---) [8, 1174, 267737] C51
110) [290761, 1943, 289600] C969 ---) [181, 3886, 2616849] C323
111) [292933, 629, 25677] C969 ---) [317, 1258, 292933] C323
112) [439081, 1991, 3088] C969 12) [193, 3982, 3951729] C969
113) [511541, 765, 18421] C969 ---) [109, 1530, 511541] C323
114) [629977, 1307, 269568] C969 ---) [13, 2614, 629977] C323
115) [640777, 835, 14112] C969 ---) [8, 1670, 640777] C57
116) [671777, 1231, 210896] C969 15) [269, 2462, 671777] C969
117) [1049473, 1439, 255312] C969 13) [197, 2878, 1049473] C969
118) [1088993, 1095, 27508] C969 ---) [13, 2190, 1088993] C323
119) [1135633, 1303, 140544] C969 ---) [61, 2606, 1135633] C323
120) [1186169, 1387, 184400] C969 21) [461, 2774, 1186169] C969
121) [1472017, 1303, 56448] C969 ---) [8, 2606, 1472017] C323
122) [1512481, 1231, 720] C969 ---) [5, 2462, 1512481] C323
123) [1678361, 1755, 350416] C969 11) [181, 3510, 1678361] C969
124) [1751041, 3971, 2368] C969 ---) [37, 7942, 15759369] C323
125) [1822673, 1591, 177152] C969 10) [173, 3182, 1822673] C969
126) [2085569, 1663, 170000] C969 2) [17, 3326, 2085569] C969
127) [2098169, 1451, 1808] C969 ---) [113, 2902, 2098169] C323
128) [2247521, 1711, 170000] C969 3) [17, 3422, 2247521] C969
129) [2518913, 1599, 9472] C969 4) [37, 3198, 2518913] C969
130) [2824097, 1711, 25856] C969 8) [101, 3422, 2824097] C969
131) [2887441, 2039, 317520] C969 ---) [5, 3597, 2887441] C323
132) [3537161, 2019, 134800] C969 18) [337, 4038, 3537161] C969
133) [4351793, 2183, 103424] C969 7) [101, 4366, 4351793] C969
134) [5451137, 2367, 37888] C969 5) [37, 4734, 5451137] C969
135) [5690777, 2491, 128576] C969 ---) [41, 4982, 5690777] C323
136) [7385449, 2963, 348480] C969 ---) [5, 5926, 7385449] C323
137) [7502377, 2995, 366912] C969 ---) [13, 5990, 7502377] C323
138) [7796449, 3727, 1523520] C969 ---) [5, 5661, 7796449] C323
139) [8609617, 2935, 1152] C969 1) [8, 5870, 8609617] C969
140) [12711497, 3683, 213248] C969 ---) [17, 7366, 12711497] C323
141) [14051369, 3763, 27200] C969 ---) [17, 7526, 14051369] C323
142) [16525001, 4067, 3872] C969 ---) [8, 8134, 16525001] C323
143) [21776537, 4667, 1088] C969 ---) [17, 9334, 21776537] C323