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 C563 non-normal (D4) quartic CM field invariants: 220 fields

K Quartic invariants Cl(OK) Igusa invariants Kr Reflex invariants Cl(OKr) Igusa invariants
1) [5, 7526, 14078249] C563 212) [14078249, 3763, 20480] C563
2) [5, 6574, 10758289] C563 ---) [10758289, 3287, 11520] C1689
3) [5, 5558, 7308121] C563 206) [7308121, 2779, 103680] C563
4) [5, 8374, 17242969] C563 215) [17242969, 4187, 72000] C563
5) [5, 8534, 18079289] C563 ---) [18079289, 4267, 32000] C1689
6) [5, 7414, 12589849] C563 210) [12589849, 3707, 288000] C563
7) [5, 5638, 7914761] C563 207) [7914761, 2819, 8000] C563
8) [5, 6457, 9063401] C563 ---) [9063401, 3539, 865280] C1689
9) [5, 6262, 8937881] C563 ---) [8937881, 3131, 216320] C1689
10) [5, 7846, 14237929] C563 213) [14237929, 3923, 288000] C563
11) [8, 4718, 5532113] C563 ---) [5532113, 2359, 8192] C7319
12) [8, 4046, 4051057] C563 202) [4051057, 2023, 10368] C563
13) [8, 3422, 2847521] C563 200) [2847521, 1711, 20000] C563
14) [8, 7366, 13523017] C563 211) [13523017, 3683, 10368] C563
15) [8, 11270, 31745033] C563 219) [31745033, 5635, 2048] C563
16) [8, 6062, 5487761] C563 204) [5487761, 3031, 924800] C563
17) [13, 8702, 17852929] C563 217) [17852929, 4351, 269568] C563
18) [13, 7766, 14890489] C563 214) [14890489, 3883, 46800] C563
19) [13, 4590, 4704593] C563 ---) [4704593, 2295, 140608] C1689
20) [13, 12158, 36946753] C563 220) [36946753, 6079, 1872] C563
21) [13, 3750, 3514793] C563 ---) [3514793, 1875, 208] C1689
22) [13, 7598, 14162833] C563 ---) [14162833, 3799, 67392] C1689
23) [13, 3846, 3597257] C563 201) [3597257, 1923, 25168] C563
24) [13, 6350, 7916593] C563 208) [7916593, 3175, 541008] C563
25) [29, 3902, 2453377] C563 199) [2453377, 1951, 338256] C563
26) [41, 6278, 8341897] C563 209) [8341897, 3139, 377856] C563
27) [41, 8486, 17992553] C563 218) [17992553, 4243, 2624] C563
28) [73, 6438, 8100713] C563 ---) [8100713, 3219, 565312] C5067
29) [73, 8438, 17631769] C563 216) [17631769, 4219, 42048] C563
30) [89, 4294, 4148233] C563 203) [4148233, 2147, 115344] C563
31) [97, 1726, 440577] C563 ---) [48953, 863, 76048] C1689
32) [97, 1338, 437861] C563 189) [437861, 669, 2425] C563
33) [97, 2151, 1027472] C563 174) [64217, 1679, 560272] C563
34) [109, 997, 228637] C563 180) [228637, 1994, 79461] C563
35) [109, 2062, 888561] C563 176) [98729, 1031, 43600] C563
36) [113, 454, 35257] C563 171) [35257, 227, 4068] C563
37) [113, 1690, 709957] C563 ---) [709957, 845, 1017] C6193
38) [149, 1462, 531977] C563 192) [531977, 731, 596] C563
39) [173, 5494, 626009] C563 ---) [626009, 2747, 1730000] C1689
40) [173, 1906, 824477] C563 194) [824477, 953, 20933] C563
41) [181, 3074, 2355853] C563 198) [2355853, 1537, 1629] C563
42) [193, 3846, 3648521] C563 ---) [3648521, 1923, 12352] C1689
43) [193, 1022, 149953] C563 178) [149953, 511, 27792] C563
44) [193, 1723, 512464] C563 170) [32029, 1801, 162313] C563
45) [197, 4894, 427681] C563 188) [427681, 2447, 1390032] C563
46) [233, 4934, 5713289] C563 ---) [5713289, 2467, 93200] C5067
47) [233, 1730, 590717] C563 193) [590717, 865, 39377] C563
48) [241, 6966, 5961689] C563 205) [5961689, 3483, 1542400] C563
49) [241, 1874, 869293] C563 195) [869293, 937, 2169] C563
50) [313, 603, 49508] C563 143) [12377, 1206, 165577] C563
51) [317, 1069, 250741] C563 181) [250741, 2138, 139797] C563
52) [353, 2371, 70276] C563 ---) [17569, 1843, 317700] C3941
53) [433, 6918, 879881] C563 196) [879881, 3459, 2771200] C563
54) [461, 1457, 530597] C563 191) [530597, 2914, 461] C563
55) [521, 1854, 325825] C563 ---) [13033, 927, 133376] C7319
56) [569, 2894, 309425] C563 144) [12377, 1447, 446096] C563
57) [593, 1490, 154157] C563 179) [154157, 745, 100217] C563
58) [617, 1159, 267796] C563 ---) [66949, 2318, 272097] C2815
59) [661, 1013, 153261] C563 165) [17029, 2026, 413125] C563
60) [661, 1245, 387341] C563 185) [387341, 2490, 661] C563
61) [673, 663, 101648] C563 131) [6353, 1326, 32977] C563
62) [677, 1282, 408173] C563 186) [408173, 641, 677] C563
63) [709, 1386, 409349] C563 187) [409349, 693, 17725] C563
64) [877, 2105, 581337] C563 133) [7177, 1783, 3508] C563
65) [1033, 4326, 447401] C563 190) [447401, 2163, 1057792] C563
66) [1069, 910, 138609] C563 160) [15401, 455, 17104] C563
67) [1453, 1085, 291037] C563 182) [291037, 2170, 13077] C563
68) [1493, 1570, 323597] C563 183) [323597, 785, 73157] C563
69) [1693, 1250, 329677] C563 184) [329677, 625, 15237] C563
70) [1693, 1990, 962937] C563 177) [106993, 995, 6772] C563
71) [1777, 927, 214388] C563 172) [53597, 1854, 1777] C563
72) [2069, 4829, 5787913] C563 162) [16033, 4827, 4378004] C563
73) [2129, 1019, 24868] C563 129) [6217, 2038, 938889] C563
74) [2269, 630, 62921] C563 173) [62921, 315, 9076] C563
75) [2269, 3878, 129321] C563 154) [14369, 1939, 907600] C563
76) [2273, 1362, 18253] C563 ---) [18253, 681, 111377] C2815
77) [2473, 1847, 748368] C563 119) [5197, 3545, 22257] C563
78) [2549, 553, 70717] C563 175) [70717, 1106, 22941] C563
79) [2621, 5209, 1823833] C563 159) [15073, 3939, 3784724] C563
80) [2621, 4925, 1549889] C563 146) [12809, 3527, 3029876] C563
81) [2797, 658, 7549] C563 135) [7549, 329, 25173] C563
82) [2801, 5682, 4026637] C563 151) [13933, 2841, 1011161] C563
83) [2833, 4447, 523764] C563 155) [14549, 6393, 5238217] C563
84) [2909, 2894, 418225] C563 164) [16729, 1447, 418896] C563
85) [2953, 2899, 1887696] C563 148) [13109, 5798, 853417] C563
86) [3217, 2823, 61328] C563 95) [3833, 3315, 630532] C563
87) [3389, 2885, 1774949] C563 157) [14669, 5770, 1223429] C563
88) [3469, 1802, 131877] C563 ---) [14653, 901, 169981] C1689
89) [3469, 4573, 4845625] C563 ---) [7753, 4967, 6119316] C1689
90) [3469, 2857, 1096177] C563 93) [3793, 3199, 2345044] C563
91) [3581, 1406, 265025] C563 140) [10601, 703, 57296] C563
92) [3637, 6029, 6336729] C563 153) [14369, 5691, 1454800] C563
93) [3793, 3199, 2345044] C563 90) [3469, 2857, 1096177] C563
94) [3833, 1858, 725053] C563 158) [14797, 929, 34497] C563
95) [3833, 3315, 630532] C563 86) [3217, 2823, 61328] C563
96) [3853, 3025, 2209633] C563 102) [4177, 4015, 3945472] C563
97) [4093, 5073, 6432809] C563 136) [7649, 3603, 1637200] C563
98) [4133, 7190, 4922537] C563 ---) [17033, 3595, 2000372] C2815
99) [4153, 4171, 228496] C563 ---) [14281, 7207, 10382500] C2815
100) [4153, 3387, 375104] C563 126) [5861, 3601, 2595625] C563
101) [4157, 6710, 15497] C563 161) [15497, 3355, 2810132] C563
102) [4177, 4015, 3945472] C563 96) [3853, 3025, 2209633] C563
103) [4241, 7322, 12028837] C563 145) [12517, 3661, 343521] C563
104) [4273, 2339, 469332] C563 147) [13037, 4678, 3593593] C563
105) [4289, 1267, 220112] C563 150) [13757, 2534, 724841] C563
106) [4297, 1479, 159056] C563 139) [9941, 2958, 1551217] C563
107) [4349, 6253, 8860625] C563 152) [14177, 5147, 69584] C563
108) [4349, 829, 162025] C563 ---) [6481, 1658, 39141] C2815
109) [4517, 582, 12409] C563 ---) [12409, 291, 18068] C5067
110) [4673, 2947, 11108] C563 ---) [2777, 2263, 1196288] C1689
111) [4721, 4498, 4585901] C563 137) [8669, 2249, 118025] C563
112) [4909, 8173, 7832601] C563 167) [17761, 5923, 8659476] C563
113) [4957, 5462, 7141113] C563 163) [16193, 2731, 79312] C563
114) [4957, 5798, 6421401] C563 156) [14561, 2899, 495700] C563
115) [5009, 5335, 5912144] C563 134) [7541, 3553, 846521] C563
116) [5101, 4690, 3846301] C563 149) [13309, 2345, 413181] C563
117) [5153, 643, 71156] C563 168) [17789, 1286, 128825] C563
118) [5197, 4897, 5702821] C563 132) [6781, 3617, 420957] C563
119) [5197, 3545, 22257] C563 77) [2473, 1847, 748368] C563
120) [5197, 569, 79641] C563 138) [8849, 1138, 5197] C563
121) [5209, 1663, 658836] C563 169) [18301, 3326, 130225] C563
122) [5233, 8047, 69604] C563 166) [17401, 8207, 1695492] C563
123) [5413, 6865, 7980777] C563 ---) [18097, 7711, 12471552] C1689
124) [5449, 4514, 1410525] C563 130) [6269, 2257, 920881] C563
125) [5573, 313, 11953] C563 141) [11953, 626, 50157] C563
126) [5861, 3601, 2595625] C563 100) [4153, 3387, 375104] C563
127) [5861, 7861, 4358353] C563 142) [12073, 6051, 23444] C563
128) [5981, 7738, 16661] C563 ---) [16661, 3869, 3738125] C1689
129) [6217, 2038, 938889] C563 73) [2129, 1019, 24868] C563
130) [6269, 2257, 920881] C563 124) [5449, 4514, 1410525] C563
131) [6353, 1326, 32977] C563 61) [673, 663, 101648] C563
132) [6781, 3617, 420957] C563 118) [5197, 4897, 5702821] C563
133) [7177, 1783, 3508] C563 64) [877, 2105, 581337] C563
134) [7541, 3553, 846521] C563 115) [5009, 5335, 5912144] C563
135) [7549, 329, 25173] C563 81) [2797, 658, 7549] C563
136) [7649, 3603, 1637200] C563 97) [4093, 5073, 6432809] C563
137) [8669, 2249, 118025] C563 111) [4721, 4498, 4585901] C563
138) [8849, 1138, 5197] C563 120) [5197, 569, 79641] C563
139) [9941, 2958, 1551217] C563 106) [4297, 1479, 159056] C563
140) [10601, 703, 57296] C563 91) [3581, 1406, 265025] C563
141) [11953, 626, 50157] C563 125) [5573, 313, 11953] C563
142) [12073, 6051, 23444] C563 127) [5861, 7861, 4358353] C563
143) [12377, 1206, 165577] C563 50) [313, 603, 49508] C563
144) [12377, 1447, 446096] C563 56) [569, 2894, 309425] C563
145) [12517, 3661, 343521] C563 103) [4241, 7322, 12028837] C563
146) [12809, 3527, 3029876] C563 80) [2621, 4925, 1549889] C563
147) [13037, 4678, 3593593] C563 104) [4273, 2339, 469332] C563
148) [13109, 5798, 853417] C563 85) [2953, 2899, 1887696] C563
149) [13309, 2345, 413181] C563 116) [5101, 4690, 3846301] C563
150) [13757, 2534, 724841] C563 105) [4289, 1267, 220112] C563
151) [13933, 2841, 1011161] C563 82) [2801, 5682, 4026637] C563
152) [14177, 5147, 69584] C563 107) [4349, 6253, 8860625] C563
153) [14369, 5691, 1454800] C563 92) [3637, 6029, 6336729] C563
154) [14369, 1939, 907600] C563 75) [2269, 3878, 129321] C563
155) [14549, 6393, 5238217] C563 83) [2833, 4447, 523764] C563
156) [14561, 2899, 495700] C563 114) [4957, 5798, 6421401] C563
157) [14669, 5770, 1223429] C563 87) [3389, 2885, 1774949] C563
158) [14797, 929, 34497] C563 94) [3833, 1858, 725053] C563
159) [15073, 3939, 3784724] C563 79) [2621, 5209, 1823833] C563
160) [15401, 455, 17104] C563 66) [1069, 910, 138609] C563
161) [15497, 3355, 2810132] C563 101) [4157, 6710, 15497] C563
162) [16033, 4827, 4378004] C563 72) [2069, 4829, 5787913] C563
163) [16193, 2731, 79312] C563 113) [4957, 5462, 7141113] C563
164) [16729, 1447, 418896] C563 84) [2909, 2894, 418225] C563
165) [17029, 2026, 413125] C563 59) [661, 1013, 153261] C563
166) [17401, 8207, 1695492] C563 122) [5233, 8047, 69604] C563
167) [17761, 5923, 8659476] C563 112) [4909, 8173, 7832601] C563
168) [17789, 1286, 128825] C563 117) [5153, 643, 71156] C563
169) [18301, 3326, 130225] C563 121) [5209, 1663, 658836] C563
170) [32029, 1801, 162313] C563 44) [193, 1723, 512464] C563
171) [35257, 227, 4068] C563 36) [113, 454, 35257] C563
172) [53597, 1854, 1777] C563 71) [1777, 927, 214388] C563
173) [62921, 315, 9076] C563 74) [2269, 630, 62921] C563
174) [64217, 1679, 560272] C563 33) [97, 2151, 1027472] C563
175) [70717, 1106, 22941] C563 78) [2549, 553, 70717] C563
176) [98729, 1031, 43600] C563 35) [109, 2062, 888561] C563
177) [106993, 995, 6772] C563 70) [1693, 1990, 962937] C563
178) [149953, 511, 27792] C563 43) [193, 1022, 149953] C563
179) [154157, 745, 100217] C563 57) [593, 1490, 154157] C563
180) [228637, 1994, 79461] C563 34) [109, 997, 228637] C563
181) [250741, 2138, 139797] C563 51) [317, 1069, 250741] C563
182) [291037, 2170, 13077] C563 67) [1453, 1085, 291037] C563
183) [323597, 785, 73157] C563 68) [1493, 1570, 323597] C563
184) [329677, 625, 15237] C563 69) [1693, 1250, 329677] C563
185) [387341, 2490, 661] C563 60) [661, 1245, 387341] C563
186) [408173, 641, 677] C563 62) [677, 1282, 408173] C563
187) [409349, 693, 17725] C563 63) [709, 1386, 409349] C563
188) [427681, 2447, 1390032] C563 45) [197, 4894, 427681] C563
189) [437861, 669, 2425] C563 32) [97, 1338, 437861] C563
190) [447401, 2163, 1057792] C563 65) [1033, 4326, 447401] C563
191) [530597, 2914, 461] C563 54) [461, 1457, 530597] C563
192) [531977, 731, 596] C563 38) [149, 1462, 531977] C563
193) [590717, 865, 39377] C563 47) [233, 1730, 590717] C563
194) [824477, 953, 20933] C563 40) [173, 1906, 824477] C563
195) [869293, 937, 2169] C563 49) [241, 1874, 869293] C563
196) [879881, 3459, 2771200] C563 53) [433, 6918, 879881] C563
197) [2062889, 1459, 16448] C563 ---) [257, 2918, 2062889] C1689
198) [2355853, 1537, 1629] C563 41) [181, 3074, 2355853] C563
199) [2453377, 1951, 338256] C563 25) [29, 3902, 2453377] C563
200) [2847521, 1711, 20000] C563 13) [8, 3422, 2847521] C563
201) [3597257, 1923, 25168] C563 23) [13, 3846, 3597257] C563
202) [4051057, 2023, 10368] C563 12) [8, 4046, 4051057] C563
203) [4148233, 2147, 115344] C563 30) [89, 4294, 4148233] C563
204) [5487761, 3031, 924800] C563 16) [8, 6062, 5487761] C563
205) [5961689, 3483, 1542400] C563 48) [241, 6966, 5961689] C563
206) [7308121, 2779, 103680] C563 3) [5, 5558, 7308121] C563
207) [7914761, 2819, 8000] C563 7) [5, 5638, 7914761] C563
208) [7916593, 3175, 541008] C563 24) [13, 6350, 7916593] C563
209) [8341897, 3139, 377856] C563 26) [41, 6278, 8341897] C563
210) [12589849, 3707, 288000] C563 6) [5, 7414, 12589849] C563
211) [13523017, 3683, 10368] C563 14) [8, 7366, 13523017] C563
212) [14078249, 3763, 20480] C563 1) [5, 7526, 14078249] C563
213) [14237929, 3923, 288000] C563 10) [5, 7846, 14237929] C563
214) [14890489, 3883, 46800] C563 18) [13, 7766, 14890489] C563
215) [17242969, 4187, 72000] C563 4) [5, 8374, 17242969] C563
216) [17631769, 4219, 42048] C563 29) [73, 8438, 17631769] C563
217) [17852929, 4351, 269568] C563 17) [13, 8702, 17852929] C563
218) [17992553, 4243, 2624] C563 27) [41, 8486, 17992553] C563
219) [31745033, 5635, 2048] C563 15) [8, 11270, 31745033] C563
220) [36946753, 6079, 1872] C563 20) [13, 12158, 36946753] C563