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 C3 x C93 non-normal (D4) quartic CM field invariants: 169 fields

K Quartic invariants Cl(OK) Igusa invariants Kr Reflex invariants Cl(OKr) Igusa invariants
1) [5, 5926, 8740649] C3 x C93 ---) [8740649, 2963, 9680] C3 x C465
2) [5, 3589, 3201929] C3 x C93 163) [3201929, 2843, 1220180] C3 x C93
3) [5, 4798, 4889921] C3 x C93 165) [4889921, 2399, 216320] C3 x C93
4) [5, 4534, 4402009] C3 x C93 164) [4402009, 2267, 184320] C3 x C93
5) [5, 3261, 2653249] C3 x C93 162) [2653249, 2527, 933120] C3 x C93
6) [8, 2174, 1006337] C3 x C93 155) [1006337, 1087, 43808] C3 x C93
7) [8, 7030, 8995993] C3 x C93 ---) [8995993, 3515, 839808] C3 x C651
8) [8, 4366, 2398001] C3 x C93 ---) [2398001, 2183, 591872] C3 x C3 x C93
9) [8, 5110, 6527737] C3 x C93 168) [6527737, 2555, 72] C3 x C93
10) [13, 3021, 861617] C3 x C93 149) [861617, 1863, 652288] C3 x C93
11) [17, 7270, 10706473] C3 x C93 169) [10706473, 3635, 626688] C3 x C93
12) [37, 774, 147401] C3 x C93 128) [147401, 387, 592] C3 x C93
13) [41, 3094, 2369593] C3 x C93 ---) [2369593, 1547, 5904] C3 x C3 x C93
14) [41, 1034, 265813] C3 x C93 131) [265813, 517, 369] C3 x C93
15) [41, 5014, 5694649] C3 x C93 167) [5694649, 2507, 147600] C3 x C93
16) [89, 5350, 5310121] C3 x C93 166) [5310121, 2675, 461376] C3 x C93
17) [97, 1627, 651088] C3 x C93 112) [40693, 1633, 575113] C3 x C93
18) [113, 539, 52036] C3 x C93 88) [13009, 1078, 82377] C3 x C93
19) [137, 2966, 1980089] C3 x C93 161) [1980089, 1483, 54800] C3 x C93
20) [197, 894, 45361] C3 x C93 ---) [45361, 447, 38612] C3 x C3 x C93
21) [229, 794, 46773] C3 x C93 ---) [5197, 397, 27709] C93
22) [229, 2429, 27673] C3 x C93 107) [27673, 2507, 14656] C3 x C93
23) [257, 662, 93113] C3 x C93 ---) [93113, 331, 4112] C93
24) [257, 1279, 408896] C3 x C93 ---) [6389, 1189, 351833] C93
25) [257, 386, 11549] C3 x C93 ---) [11549, 193, 6425] C93
26) [257, 2747, 1580608] C3 x C93 ---) [24697, 1547, 592128] C3 x C279
27) [373, 781, 10657] C3 x C93 82) [10657, 1562, 567333] C3 x C93
28) [457, 826, 168741] C3 x C93 100) [18749, 413, 457] C3 x C93
29) [509, 1389, 460825] C3 x C93 ---) [18433, 2778, 86021] C3 x C465
30) [601, 918, 172217] C3 x C93 ---) [172217, 459, 9616] C3 x C3 x C93
31) [653, 5638, 6901961] C3 x C93 118) [57041, 2819, 261200] C3 x C93
32) [677, 1718, 44633] C3 x C93 115) [44633, 859, 173312] C3 x C93
33) [733, 569, 80757] C3 x C93 ---) [997, 725, 59373] C93
34) [733, 926, 26721] C3 x C93 ---) [2969, 463, 46912] C93
35) [733, 910, 19377] C3 x C93 ---) [2153, 455, 46912] C465
36) [773, 517, 66629] C3 x C93 120) [66629, 1034, 773] C3 x C93
37) [853, 950, 102793] C3 x C93 ---) [102793, 475, 30708] C3 x C465
38) [853, 1357, 101889] C3 x C93 ---) [11321, 2714, 1433893] C3 x C3 x C465
39) [857, 943, 42128] C3 x C93 54) [2633, 1595, 3428] C3 x C93
40) [941, 2318, 1328225] C3 x C93 117) [53129, 1159, 3764] C3 x C93
41) [953, 2114, 15581] C3 x C93 95) [15581, 1057, 275417] C3 x C93
42) [997, 1685, 111357] C3 x C93 85) [12373, 3370, 2393797] C3 x C93
43) [997, 2061, 8849] C3 x C93 78) [8849, 2191, 1020928] C3 x C93
44) [1013, 442, 44789] C3 x C93 116) [44789, 221, 1013] C3 x C93
45) [1097, 695, 87572] C3 x C93 103) [21893, 1390, 132737] C3 x C93
46) [1489, 655, 106884] C3 x C93 ---) [2969, 1310, 1489] C93
47) [1789, 1361, 33273] C3 x C93 60) [3697, 2431, 1402576] C3 x C93
48) [2053, 141, 4457] C3 x C93 62) [4457, 282, 2053] C3 x C93
49) [2089, 351, 17744] C3 x C93 ---) [1109, 702, 52225] C93
50) [2089, 2382, 582881] C3 x C93 ---) [3449, 1191, 208900] C93
51) [2269, 201, 9533] C3 x C93 79) [9533, 402, 2269] C3 x C93
52) [2341, 4569, 5148125] C3 x C93 75) [8237, 2609, 1238389] C3 x C93
53) [2557, 2037, 499733] C3 x C93 ---) [2957, 2377, 1352653] C93
54) [2633, 1595, 3428] C3 x C93 39) [857, 943, 42128] C3 x C93
55) [2633, 3346, 1945837] C3 x C93 72) [6733, 1673, 213273] C3 x C93
56) [2713, 2122, 593973] C3 x C93 ---) [7333, 1061, 132937] C93
57) [2713, 1063, 265536] C3 x C93 ---) [461, 589, 2713] C93
58) [3169, 1098, 288725] C3 x C93 83) [11549, 549, 3169] C3 x C93
59) [3461, 1026, 249325] C3 x C93 80) [9973, 513, 3461] C3 x C93
60) [3697, 2431, 1402576] C3 x C93 47) [1789, 1361, 33273] C3 x C93
61) [3889, 6534, 4450889] C3 x C93 ---) [15401, 3267, 1555600] C93
62) [4457, 282, 2053] C3 x C93 48) [2053, 141, 4457] C3 x C93
63) [4637, 1585, 14813] C3 x C93 93) [14813, 3170, 2452973] C3 x C93
64) [4637, 5630, 7627457] C3 x C93 74) [7937, 2815, 74192] C3 x C93
65) [4649, 2275, 958016] C3 x C93 94) [14969, 4550, 1343561] C3 x C93
66) [4877, 7546, 14197] C3 x C93 ---) [14197, 3773, 3555333] C3 x C3 x C93
67) [4933, 181, 6957] C3 x C93 ---) [773, 362, 4933] C93
68) [4937, 867, 186688] C3 x C93 ---) [2917, 1734, 4937] C3 x C3 x C93
69) [5261, 1237, 223397] C3 x C93 ---) [773, 1813, 5261] C93
70) [5821, 105, 1301] C3 x C93 ---) [1301, 210, 5821] C93
71) [6133, 386, 12717] C3 x C93 ---) [157, 193, 6133] C93
72) [6733, 1673, 213273] C3 x C93 55) [2633, 3346, 1945837] C3 x C93
73) [7537, 515, 49348] C3 x C93 ---) [73, 695, 120592] C93
74) [7937, 2815, 74192] C3 x C93 64) [4637, 5630, 7627457] C3 x C93
75) [8237, 2609, 1238389] C3 x C93 52) [2341, 4569, 5148125] C3 x C93
76) [8713, 3299, 348736] C3 x C93 ---) [5449, 6598, 9488457] C93
77) [8837, 473, 701] C3 x C93 ---) [701, 946, 220925] C93
78) [8849, 2191, 1020928] C3 x C93 43) [997, 2061, 8849] C3 x C93
79) [9533, 402, 2269] C3 x C93 51) [2269, 201, 9533] C3 x C93
80) [9973, 513, 3461] C3 x C93 59) [3461, 1026, 249325] C3 x C93
81) [10333, 3293, 827773] C3 x C93 ---) [2293, 4745, 10333] C93
82) [10657, 1562, 567333] C3 x C93 27) [373, 781, 10657] C3 x C93
83) [11549, 549, 3169] C3 x C93 58) [3169, 1098, 288725] C3 x C93
84) [11821, 1750, 9081] C3 x C93 ---) [1009, 875, 189136] C651
85) [12373, 3370, 2393797] C3 x C93 42) [997, 1685, 111357] C3 x C93
86) [12401, 2286, 1108033] C3 x C93 ---) [1153, 1143, 49604] C93
87) [12401, 1966, 767873] C3 x C93 ---) [2657, 983, 49604] C93
88) [13009, 1078, 82377] C3 x C93 18) [113, 539, 52036] C3 x C93
89) [13537, 3047, 2046928] C3 x C93 ---) [757, 2561, 1637977] C93
90) [13537, 1571, 45072] C3 x C93 ---) [313, 1415, 487332] C93
91) [13577, 6227, 2195984] C3 x C93 ---) [2801, 3263, 2661092] C93
92) [13577, 731, 130196] C3 x C93 ---) [269, 1462, 13577] C93
93) [14813, 3170, 2452973] C3 x C93 63) [4637, 1585, 14813] C3 x C93
94) [14969, 4550, 1343561] C3 x C93 65) [4649, 2275, 958016] C3 x C93
95) [15581, 1057, 275417] C3 x C93 41) [953, 2114, 15581] C3 x C93
96) [16553, 1342, 185393] C3 x C93 ---) [1097, 671, 66212] C93
97) [17053, 2165, 1133437] C3 x C93 ---) [613, 2465, 17053] C93
98) [17929, 2374, 261513] C3 x C93 ---) [593, 1187, 286864] C93
99) [18661, 2254, 75825] C3 x C93 ---) [337, 1127, 298576] C93
100) [18749, 413, 457] C3 x C93 28) [457, 826, 168741] C3 x C93
101) [19469, 602, 12725] C3 x C93 ---) [509, 301, 19469] C93
102) [21557, 1333, 7693] C3 x C93 ---) [157, 1885, 194013] C93
103) [21893, 1390, 132737] C3 x C93 45) [1097, 695, 87572] C3 x C93
104) [23909, 1374, 89425] C3 x C93 ---) [73, 687, 95636] C93
105) [25717, 642, 173] C3 x C93 ---) [173, 321, 25717] C93
106) [26113, 611, 34576] C3 x C93 ---) [2161, 1222, 235017] C93
107) [27673, 2507, 14656] C3 x C93 22) [229, 2429, 27673] C3 x C93
108) [31513, 551, 4996] C3 x C93 ---) [1249, 1102, 283617] C93
109) [38993, 1203, 118096] C3 x C93 ---) [61, 1277, 350937] C93
110) [39397, 2169, 929909] C3 x C93 ---) [149, 1553, 39397] C93
111) [40093, 1386, 319877] C3 x C93 ---) [173, 693, 40093] C93
112) [40693, 1633, 575113] C3 x C93 17) [97, 1627, 651088] C3 x C93
113) [43717, 1113, 36461] C3 x C93 ---) [101, 2117, 1092925] C93
114) [44617, 1018, 80613] C3 x C93 ---) [53, 509, 44617] C93
115) [44633, 859, 173312] C3 x C93 32) [677, 1718, 44633] C3 x C93
116) [44789, 221, 1013] C3 x C93 44) [1013, 442, 44789] C3 x C93
117) [53129, 1159, 3764] C3 x C93 40) [941, 2318, 1328225] C3 x C93
118) [57041, 2819, 261200] C3 x C93 31) [653, 5638, 6901961] C3 x C93
119) [61861, 381, 20825] C3 x C93 ---) [17, 762, 61861] C93
120) [66629, 1034, 773] C3 x C93 36) [773, 517, 66629] C3 x C93
121) [76081, 277, 162] C3 x C93 ---) [8, 554, 76081] C93
122) [80221, 1194, 35525] C3 x C93 ---) [29, 597, 80221] C93
123) [89657, 387, 15028] C3 x C93 ---) [13, 774, 89657] C93
124) [93077, 953, 17629] C3 x C93 ---) [61, 1906, 837693] C93
125) [108677, 365, 6137] C3 x C93 ---) [17, 730, 108677] C93
126) [111857, 407, 13448] C3 x C93 ---) [8, 814, 111857] C93
127) [138821, 445, 14801] C3 x C93 ---) [41, 890, 138821] C93
128) [147401, 387, 592] C3 x C93 12) [37, 774, 147401] C3 x C93
129) [155821, 1594, 11925] C3 x C93 ---) [53, 797, 155821] C93
130) [237361, 519, 8000] C3 x C93 ---) [5, 1038, 237361] C93
131) [265813, 517, 369] C3 x C93 14) [41, 1034, 265813] C3 x C93
132) [312601, 763, 67392] C3 x C93 ---) [13, 1526, 312601] C93
133) [338909, 681, 31213] C3 x C93 ---) [13, 1362, 338909] C93
134) [372629, 2153, 320437] C3 x C93 ---) [13, 1221, 372629] C93
135) [400849, 1979, 77200] C3 x C93 ---) [193, 3958, 3607641] C93
136) [438233, 1307, 317504] C3 x C93 ---) [41, 2614, 438233] C93
137) [448397, 2285, 296413] C3 x C93 ---) [13, 1341, 448397] C93
138) [463261, 681, 125] C3 x C93 ---) [5, 1362, 463261] C93
139) [502501, 709, 45] C3 x C93 ---) [5, 1418, 502501] C93
140) [547241, 755, 5696] C3 x C93 ---) [89, 1510, 547241] C93
141) [550961, 1031, 128000] C3 x C93 ---) [5, 1493, 550961] C93
142) [640529, 847, 19220] C3 x C93 ---) [5, 1694, 640529] C93
143) [644729, 803, 20] C3 x C93 ---) [5, 1606, 644729] C93
144) [660941, 1681, 541205] C3 x C93 ---) [5, 1753, 660941] C93
145) [758617, 923, 23328] C3 x C93 ---) [8, 1846, 758617] C93
146) [807941, 1589, 429245] C3 x C93 ---) [5, 1837, 807941] C93
147) [826621, 1049, 68445] C3 x C93 ---) [5, 1977, 826621] C93
148) [861001, 1507, 352512] C3 x C93 ---) [17, 3014, 861001] C93
149) [861617, 1863, 652288] C3 x C93 10) [13, 3021, 861617] C3 x C93
150) [876181, 1149, 111005] C3 x C93 ---) [5, 1957, 876181] C93
151) [879721, 1017, 38642] C3 x C93 ---) [8, 2034, 879721] C93
152) [892057, 2203, 990288] C3 x C93 ---) [13, 2705, 892057] C93
153) [930389, 1997, 764405] C3 x C93 ---) [5, 2081, 930389] C93
154) [996973, 3485, 793117] C3 x C93 ---) [13, 1997, 996973] C93
155) [1006337, 1087, 43808] C3 x C93 6) [8, 2174, 1006337] C3 x C93
156) [1007417, 1067, 32768] C3 x C93 ---) [8, 2134, 1007417] C93
157) [1062877, 1033, 1053] C3 x C93 ---) [13, 2066, 1062877] C93
158) [1161481, 1091, 7200] C3 x C93 ---) [8, 2182, 1161481] C93
159) [1452229, 1653, 320045] C3 x C93 ---) [5, 2429, 1452229] C93
160) [1556069, 1733, 361805] C3 x C93 ---) [5, 2509, 1556069] C93
161) [1980089, 1483, 54800] C3 x C93 19) [137, 2966, 1980089] C3 x C93
162) [2653249, 2527, 933120] C3 x C93 5) [5, 3261, 2653249] C3 x C93
163) [3201929, 2843, 1220180] C3 x C93 2) [5, 3589, 3201929] C3 x C93
164) [4402009, 2267, 184320] C3 x C93 4) [5, 4534, 4402009] C3 x C93
165) [4889921, 2399, 216320] C3 x C93 3) [5, 4798, 4889921] C3 x C93
166) [5310121, 2675, 461376] C3 x C93 16) [89, 5350, 5310121] C3 x C93
167) [5694649, 2507, 147600] C3 x C93 15) [41, 5014, 5694649] C3 x C93
168) [6527737, 2555, 72] C3 x C93 9) [8, 5110, 6527737] C3 x C93
169) [10706473, 3635, 626688] C3 x C93 11) [17, 7270, 10706473] C3 x C93