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 529 non-normal (D4) quartic CM field invariants: 232 fields

K Quartic invariants Cl(OK) Igusa invariants Kr Reflex invariants Cl(OKr) Igusa invariants
1) [5, 9494, 21530489] C529 227) [21530489, 4747, 250880] C529
2) [5, 8246, 16487129] C529 225) [16487129, 4123, 128000] C529
3) [5, 6494, 8884129] C529 214) [8884129, 3247, 414720] C529
4) [5, 7558, 14218121] C529 221) [14218121, 3779, 15680] C529
5) [5, 5806, 8139409] C529 212) [8139409, 2903, 72000] C529
6) [5, 7934, 15655169] C529 223) [15655169, 3967, 20480] C529
7) [5, 6302, 9744481] C529 216) [9744481, 3151, 46080] C529
8) [5, 9646, 23157649] C529 228) [23157649, 4823, 25920] C529
9) [5, 6382, 10054481] C529 ---) [10054481, 3191, 32000] C1587
10) [5, 5157, 6630961] C529 210) [6630961, 3719, 1800000] C529
11) [5, 7102, 11809601] C529 219) [11809601, 3551, 200000] C529
12) [8, 4078, 3616721] C529 202) [3616721, 2039, 135200] C529
13) [8, 4654, 5414417] C529 207) [5414417, 2327, 128] C529
14) [8, 2494, 1513537] C529 193) [1513537, 1247, 10368] C529
15) [8, 3614, 2274017] C529 198) [2274017, 1807, 247808] C529
16) [8, 10006, 24402809] C529 ---) [24402809, 5003, 156800] C1587
17) [8, 4814, 4300657] C529 ---) [4300657, 2407, 373248] C1587
18) [8, 5038, 3691153] C529 ---) [3691153, 2519, 663552] C16399
19) [8, 3306, 1701361] C529 194) [1701361, 1653, 257762] C529
20) [8, 4074, 2157361] C529 197) [2157361, 2037, 498002] C529
21) [8, 8806, 19367977] C529 226) [19367977, 4403, 4608] C529
22) [8, 11542, 32746873] C529 ---) [32746873, 5771, 139392] C1587
23) [8, 3934, 3738017] C529 ---) [3738017, 1967, 32768] C1587
24) [8, 8806, 15901609] C529 224) [15901609, 4403, 871200] C529
25) [8, 6590, 6380993] C529 209) [6380993, 3295, 1119008] C529
26) [13, 4182, 4358969] C529 206) [4358969, 2091, 3328] C529
27) [13, 2062, 1046113] C529 ---) [1046113, 1031, 4212] C1587
28) [13, 4854, 4129817] C529 205) [4129817, 2427, 440128] C529
29) [13, 3486, 3024737] C529 201) [3024737, 1743, 3328] C529
30) [17, 11398, 32408969] C529 232) [32408969, 5699, 17408] C529
31) [17, 9814, 24039481] C529 230) [24039481, 4907, 9792] C529
32) [17, 7414, 13585177] C529 ---) [13585177, 3707, 39168] C70357
33) [17, 9782, 23186393] C529 229) [23186393, 4891, 183872] C529
34) [17, 9878, 24209849] C529 231) [24209849, 4939, 45968] C529
35) [17, 2038, 992393] C529 190) [992393, 1019, 11492] C529
36) [29, 2866, 2002333] C529 ---) [2002333, 1433, 12789] C1587
37) [29, 6230, 9389561] C529 215) [9389561, 3115, 78416] C529
38) [37, 4550, 3811657] C529 204) [3811657, 2275, 340992] C529
39) [37, 1806, 813041] C529 187) [813041, 903, 592] C529
40) [37, 2022, 962921] C529 188) [962921, 1011, 14800] C529
41) [37, 7262, 13098913] C529 220) [13098913, 3631, 21312] C529
42) [41, 7606, 14294873] C529 222) [14294873, 3803, 41984] C529
43) [41, 2882, 2076317] C529 196) [2076317, 1441, 41] C529
44) [53, 1990, 986633] C529 189) [986633, 995, 848] C529
45) [61, 2322, 1195421] C529 ---) [1195421, 1161, 38125] C1587
46) [61, 2178, 1185677] C529 ---) [1185677, 1089, 61] C2645
47) [73, 5526, 7559417] C529 211) [7559417, 2763, 18688] C529
48) [89, 518, 65657] C529 ---) [65657, 259, 356] C3703
49) [89, 9334, 19502489] C529 ---) [19502489, 4667, 569600] C1587
50) [89, 4342, 2434841] C529 200) [2434841, 2171, 569600] C529
51) [89, 6598, 10860617] C529 218) [10860617, 3299, 5696] C529
52) [97, 1803, 396548] C529 ---) [99137, 2903, 99328] C2645
53) [97, 5958, 8477129] C529 213) [8477129, 2979, 99328] C529
54) [101, 2122, 1092997] C529 ---) [1092997, 1061, 8181] C3703
55) [109, 12662, 39830425] C529 ---) [1593217, 6331, 62784] C7935
56) [113, 510, 36097] C529 173) [36097, 255, 7232] C529
57) [113, 2122, 1049333] C529 ---) [1049333, 1061, 19097] C2645
58) [113, 5254, 5483657] C529 208) [5483657, 2627, 354368] C529
59) [113, 6646, 10319129] C529 217) [10319129, 3323, 180800] C529
60) [137, 2074, 1048517] C529 191) [1048517, 1037, 6713] C529
61) [137, 1462, 41161] C529 175) [41161, 731, 123300] C529
62) [149, 2510, 1536881] C529 ---) [1536881, 1255, 9536] C37559
63) [173, 2330, 1301173] C529 192) [1301173, 1165, 14013] C529
64) [193, 1455, 422672] C529 171) [26417, 1839, 521872] C529
65) [193, 11638, 33811353] C529 203) [3756817, 5819, 12352] C529
66) [193, 9142, 20696409] C529 199) [2299601, 4571, 49408] C529
67) [197, 8854, 19396601] C529 183) [395849, 4427, 50432] C529
68) [233, 882, 193549] C529 178) [193549, 441, 233] C529
69) [277, 2318, 705073] C529 185) [705073, 1159, 159552] C529
70) [277, 2261, 393777] C529 ---) [43753, 3515, 2552832] C5819
71) [409, 1114, 295525] C529 ---) [11821, 557, 3681] C1587
72) [433, 1447, 405568] C529 141) [6337, 1435, 500548] C529
73) [449, 1027, 56132] C529 162) [14033, 2054, 830201] C529
74) [457, 714, 125621] C529 177) [125621, 357, 457] C529
75) [461, 1270, 373721] C529 182) [373721, 635, 7376] C529
76) [593, 2758, 1749833] C529 195) [1749833, 1379, 37952] C529
77) [593, 1283, 25924] C529 ---) [6481, 1763, 192132] C2645
78) [601, 1163, 85572] C529 98) [2377, 1003, 117796] C529
79) [613, 1730, 726157] C529 186) [726157, 865, 5517] C529
80) [677, 1165, 325597] C529 181) [325597, 2330, 54837] C529
81) [773, 1093, 255181] C529 179) [255181, 2186, 173925] C529
82) [829, 1409, 479533] C529 184) [479533, 2818, 67149] C529
83) [877, 545, 63513] C529 ---) [7057, 1090, 42973] C11109
84) [977, 1735, 213008] C529 ---) [13313, 3470, 2158193] C3703
85) [1097, 1959, 860416] C529 108) [3361, 1119, 70208] C529
86) [1097, 1358, 443489] C529 ---) [443489, 679, 4388] C2645
87) [1097, 1258, 40213] C529 174) [40213, 629, 88857] C529
88) [1153, 2639, 1104336] C529 143) [7669, 1721, 508473] C529
89) [1201, 2355, 1278116] C529 142) [6521, 2783, 1921600] C529
90) [1201, 1134, 302273] C529 180) [302273, 567, 4804] C529
91) [1777, 883, 119844] C529 107) [3329, 1766, 300313] C529
92) [2053, 594, 79997] C529 ---) [79997, 297, 2053] C2645
93) [2113, 3230, 1391137] C529 158) [11497, 1615, 304272] C529
94) [2137, 4627, 530676] C529 164) [14741, 3537, 1797217] C529
95) [2221, 1509, 368825] C529 165) [14753, 3018, 801781] C529
96) [2281, 1339, 283428] C529 ---) [7873, 2678, 659209] C4761
97) [2309, 3881, 343025] C529 161) [13721, 4235, 2669204] C529
98) [2377, 1003, 117796] C529 78) [601, 1163, 85572] C529
99) [2437, 438, 8969] C529 147) [8969, 219, 9748] C529
100) [2621, 2598, 639001] C529 ---) [5281, 1299, 262100] C1587
101) [2633, 2551, 820544] C529 ---) [12821, 5102, 3225425] C1587
102) [2657, 1627, 421988] C529 ---) [2153, 1795, 520772] C2645
103) [2689, 798, 116177] C529 176) [116177, 399, 10756] C529
104) [2801, 3811, 3624628] C529 170) [18493, 7622, 25209] C529
105) [2897, 1743, 63508] C529 ---) [15877, 3486, 2784017] C6877
106) [2953, 5007, 154064] C529 150) [9629, 2857, 1845625] C529
107) [3329, 1766, 300313] C529 91) [1777, 883, 119844] C529
108) [3361, 1119, 70208] C529 85) [1097, 1959, 860416] C529
109) [3373, 4941, 10889] C529 ---) [10889, 4303, 2644432] C1587
110) [3389, 4670, 1060081] C529 ---) [8761, 2335, 1098036] C14283
111) [3413, 3417, 522193] C529 153) [10657, 5355, 4928372] C529
112) [3457, 3399, 2845952] C529 157) [11117, 6765, 7636513] C529
113) [3457, 2311, 795024] C529 ---) [5521, 4622, 2160625] C4761
114) [3517, 4774, 70569] C529 144) [7841, 2387, 1406800] C529
115) [3637, 381, 35381] C529 172) [35381, 762, 3637] C529
116) [3637, 4841, 5530581] C529 159) [12541, 4829, 32733] C529
117) [3677, 7229, 907529] C529 ---) [18521, 5267, 2485652] C1587
118) [3761, 7802, 15202757] C529 169) [18077, 3901, 3761] C529
119) [4013, 2261, 1108481] C529 149) [9161, 4522, 678197] C529
120) [4049, 4639, 277328] C529 167) [17333, 7897, 15066329] C529
121) [4217, 2834, 1586189] C529 160) [13109, 1417, 105425] C529
122) [4217, 2611, 100816] C529 140) [6301, 5169, 5165825] C529
123) [4241, 7402, 3094901] C529 154) [10709, 3701, 2650625] C529
124) [4261, 2741, 258025] C529 151) [10321, 5482, 6480981] C529
125) [4373, 7986, 5011549] C529 168) [17341, 3993, 2733125] C529
126) [4549, 1357, 131697] C529 163) [14633, 2714, 1314661] C529
127) [4549, 5837, 7806861] C529 155) [10709, 4245, 4549] C529
128) [4621, 4477, 2006077] C529 137) [5557, 4837, 1335469] C529
129) [4621, 5210, 113301] C529 ---) [12589, 2605, 1668181] C5819
130) [4621, 4981, 5693125] C529 148) [9109, 4297, 4621] C529
131) [4721, 3455, 1000256] C529 ---) [15629, 6910, 7936001] C4761
132) [4721, 4903, 60212] C529 166) [15053, 7309, 13261289] C529
133) [4813, 4469, 4558617] C529 152) [10337, 7539, 6949972] C529
134) [4957, 689, 117441] C529 ---) [13049, 1378, 4957] C3703
135) [5197, 3969, 8009] C529 145) [8009, 5723, 6007732] C529
136) [5557, 5869, 6275961] C529 146) [8609, 4143, 2222800] C529
137) [5557, 4837, 1335469] C529 128) [4621, 4477, 2006077] C529
138) [5669, 3518, 1642817] C529 ---) [13577, 1759, 362816] C1587
139) [5801, 7522, 3912157] C529 156) [10837, 3761, 2558241] C529
140) [6301, 5169, 5165825] C529 122) [4217, 2611, 100816] C529
141) [6337, 1435, 500548] C529 72) [433, 1447, 405568] C529
142) [6521, 2783, 1921600] C529 89) [1201, 2355, 1278116] C529
143) [7669, 1721, 508473] C529 88) [1153, 2639, 1104336] C529
144) [7841, 2387, 1406800] C529 114) [3517, 4774, 70569] C529
145) [8009, 5723, 6007732] C529 135) [5197, 3969, 8009] C529
146) [8609, 4143, 2222800] C529 136) [5557, 5869, 6275961] C529
147) [8969, 219, 9748] C529 99) [2437, 438, 8969] C529
148) [9109, 4297, 4621] C529 130) [4621, 4981, 5693125] C529
149) [9161, 4522, 678197] C529 119) [4013, 2261, 1108481] C529
150) [9629, 2857, 1845625] C529 106) [2953, 5007, 154064] C529
151) [10321, 5482, 6480981] C529 124) [4261, 2741, 258025] C529
152) [10337, 7539, 6949972] C529 133) [4813, 4469, 4558617] C529
153) [10657, 5355, 4928372] C529 111) [3413, 3417, 522193] C529
154) [10709, 3701, 2650625] C529 123) [4241, 7402, 3094901] C529
155) [10709, 4245, 4549] C529 127) [4549, 5837, 7806861] C529
156) [10837, 3761, 2558241] C529 139) [5801, 7522, 3912157] C529
157) [11117, 6765, 7636513] C529 112) [3457, 3399, 2845952] C529
158) [11497, 1615, 304272] C529 93) [2113, 3230, 1391137] C529
159) [12541, 4829, 32733] C529 116) [3637, 4841, 5530581] C529
160) [13109, 1417, 105425] C529 121) [4217, 2834, 1586189] C529
161) [13721, 4235, 2669204] C529 97) [2309, 3881, 343025] C529
162) [14033, 2054, 830201] C529 73) [449, 1027, 56132] C529
163) [14633, 2714, 1314661] C529 126) [4549, 1357, 131697] C529
164) [14741, 3537, 1797217] C529 94) [2137, 4627, 530676] C529
165) [14753, 3018, 801781] C529 95) [2221, 1509, 368825] C529
166) [15053, 7309, 13261289] C529 132) [4721, 4903, 60212] C529
167) [17333, 7897, 15066329] C529 120) [4049, 4639, 277328] C529
168) [17341, 3993, 2733125] C529 125) [4373, 7986, 5011549] C529
169) [18077, 3901, 3761] C529 118) [3761, 7802, 15202757] C529
170) [18493, 7622, 25209] C529 104) [2801, 3811, 3624628] C529
171) [26417, 1839, 521872] C529 64) [193, 1455, 422672] C529
172) [35381, 762, 3637] C529 115) [3637, 381, 35381] C529
173) [36097, 255, 7232] C529 56) [113, 510, 36097] C529
174) [40213, 629, 88857] C529 87) [1097, 1258, 40213] C529
175) [41161, 731, 123300] C529 61) [137, 1462, 41161] C529
176) [116177, 399, 10756] C529 103) [2689, 798, 116177] C529
177) [125621, 357, 457] C529 74) [457, 714, 125621] C529
178) [193549, 441, 233] C529 68) [233, 882, 193549] C529
179) [255181, 2186, 173925] C529 81) [773, 1093, 255181] C529
180) [302273, 567, 4804] C529 90) [1201, 1134, 302273] C529
181) [325597, 2330, 54837] C529 80) [677, 1165, 325597] C529
182) [373721, 635, 7376] C529 75) [461, 1270, 373721] C529
183) [395849, 4427, 50432] C529 67) [197, 8854, 19396601] C529
184) [479533, 2818, 67149] C529 82) [829, 1409, 479533] C529
185) [705073, 1159, 159552] C529 69) [277, 2318, 705073] C529
186) [726157, 865, 5517] C529 79) [613, 1730, 726157] C529
187) [813041, 903, 592] C529 39) [37, 1806, 813041] C529
188) [962921, 1011, 14800] C529 40) [37, 2022, 962921] C529
189) [986633, 995, 848] C529 44) [53, 1990, 986633] C529
190) [992393, 1019, 11492] C529 35) [17, 2038, 992393] C529
191) [1048517, 1037, 6713] C529 60) [137, 2074, 1048517] C529
192) [1301173, 1165, 14013] C529 63) [173, 2330, 1301173] C529
193) [1513537, 1247, 10368] C529 14) [8, 2494, 1513537] C529
194) [1701361, 1653, 257762] C529 19) [8, 3306, 1701361] C529
195) [1749833, 1379, 37952] C529 76) [593, 2758, 1749833] C529
196) [2076317, 1441, 41] C529 43) [41, 2882, 2076317] C529
197) [2157361, 2037, 498002] C529 20) [8, 4074, 2157361] C529
198) [2274017, 1807, 247808] C529 15) [8, 3614, 2274017] C529
199) [2299601, 4571, 49408] C529 66) [193, 9142, 20696409] C529
200) [2434841, 2171, 569600] C529 50) [89, 4342, 2434841] C529
201) [3024737, 1743, 3328] C529 29) [13, 3486, 3024737] C529
202) [3616721, 2039, 135200] C529 12) [8, 4078, 3616721] C529
203) [3756817, 5819, 12352] C529 65) [193, 11638, 33811353] C529
204) [3811657, 2275, 340992] C529 38) [37, 4550, 3811657] C529
205) [4129817, 2427, 440128] C529 28) [13, 4854, 4129817] C529
206) [4358969, 2091, 3328] C529 26) [13, 4182, 4358969] C529
207) [5414417, 2327, 128] C529 13) [8, 4654, 5414417] C529
208) [5483657, 2627, 354368] C529 58) [113, 5254, 5483657] C529
209) [6380993, 3295, 1119008] C529 25) [8, 6590, 6380993] C529
210) [6630961, 3719, 1800000] C529 10) [5, 5157, 6630961] C529
211) [7559417, 2763, 18688] C529 47) [73, 5526, 7559417] C529
212) [8139409, 2903, 72000] C529 5) [5, 5806, 8139409] C529
213) [8477129, 2979, 99328] C529 53) [97, 5958, 8477129] C529
214) [8884129, 3247, 414720] C529 3) [5, 6494, 8884129] C529
215) [9389561, 3115, 78416] C529 37) [29, 6230, 9389561] C529
216) [9744481, 3151, 46080] C529 7) [5, 6302, 9744481] C529
217) [10319129, 3323, 180800] C529 59) [113, 6646, 10319129] C529
218) [10860617, 3299, 5696] C529 51) [89, 6598, 10860617] C529
219) [11809601, 3551, 200000] C529 11) [5, 7102, 11809601] C529
220) [13098913, 3631, 21312] C529 41) [37, 7262, 13098913] C529
221) [14218121, 3779, 15680] C529 4) [5, 7558, 14218121] C529
222) [14294873, 3803, 41984] C529 42) [41, 7606, 14294873] C529
223) [15655169, 3967, 20480] C529 6) [5, 7934, 15655169] C529
224) [15901609, 4403, 871200] C529 24) [8, 8806, 15901609] C529
225) [16487129, 4123, 128000] C529 2) [5, 8246, 16487129] C529
226) [19367977, 4403, 4608] C529 21) [8, 8806, 19367977] C529
227) [21530489, 4747, 250880] C529 1) [5, 9494, 21530489] C529
228) [23157649, 4823, 25920] C529 8) [5, 9646, 23157649] C529
229) [23186393, 4891, 183872] C529 33) [17, 9782, 23186393] C529
230) [24039481, 4907, 9792] C529 31) [17, 9814, 24039481] C529
231) [24209849, 4939, 45968] C529 34) [17, 9878, 24209849] C529
232) [32408969, 5699, 17408] C529 30) [17, 11398, 32408969] C529