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 C815 non-normal (D4) quartic CM field invariants: 115 fields

K Quartic invariants Cl(OK) Igusa invariants Kr Reflex invariants Cl(OKr) Igusa invariants
1) [8, 6398, 10231553] C815 115) [10231553, 3199, 512] C815
2) [8, 5054, 6382529] C815 114) [6382529, 2527, 800] C815
3) [13, 6366, 10128161] C815 ---) [10128161, 3183, 832] C5 x C815
4) [17, 2158, 1159889] C815 104) [1159889, 1079, 1088] C815
5) [41, 966, 232633] C815 95) [232633, 483, 164] C815
6) [41, 2894, 1044209] C815 ---) [1044209, 1447, 262400] C5 x C8965
7) [61, 3174, 2502953] C815 113) [2502953, 1587, 3904] C815
8) [101, 3254, 2233433] C815 112) [2233433, 1627, 103424] C815
9) [137, 2351, 775952] C815 90) [48497, 1607, 633488] C815
10) [149, 3206, 1415753] C815 106) [1415753, 1603, 288464] C815
11) [157, 1782, 753689] C815 102) [753689, 891, 10048] C815
12) [157, 1230, 338033] C815 98) [338033, 615, 10048] C815
13) [173, 2510, 1032497] C815 103) [1032497, 1255, 135632] C815
14) [233, 4150, 3574937] C815 ---) [3574937, 2075, 182672] C2445
15) [241, 1278, 22721] C815 ---) [22721, 639, 96400] C2445
16) [281, 2638, 1667825] C815 92) [66713, 1319, 17984] C815
17) [401, 346, 15493] C815 ---) [15493, 173, 3609] C163
18) [401, 2054, 413129] C815 ---) [413129, 1027, 160400] C163
19) [401, 775, 142036] C815 87) [35509, 1550, 32481] C815
20) [409, 1074, 286733] C815 96) [286733, 537, 409] C815
21) [461, 1462, 504857] C815 100) [504857, 731, 7376] C815
22) [557, 1665, 692917] C815 101) [692917, 3330, 557] C815
23) [757, 822, 120473] C815 93) [120473, 411, 12112] C815
24) [881, 1039, 259088] C815 79) [16193, 2078, 43169] C815
25) [1109, 1245, 307381] C815 97) [307381, 2490, 320501] C815
26) [1429, 741, 34025] C815 ---) [1361, 1482, 412981] C163
27) [1429, 1329, 3929] C815 ---) [3929, 2179, 966004] C163
28) [2153, 1339, 327124] C815 ---) [1669, 1537, 19377] C163
29) [2153, 551, 10772] C815 ---) [2693, 1102, 260513] C163
30) [2297, 3823, 249104] C815 77) [15569, 5347, 5742500] C815
31) [2377, 1675, 529668] C815 73) [14713, 3350, 686953] C815
32) [2393, 1190, 9433] C815 63) [9433, 595, 86148] C815
33) [2753, 1699, 638372] C815 38) [3257, 3398, 333113] C815
34) [3089, 1346, 341725] C815 71) [13669, 673, 27801] C815
35) [3169, 5047, 1170100] C815 66) [11701, 5317, 3882025] C815
36) [3217, 2578, 619213] C815 70) [12637, 1289, 260577] C815
37) [3253, 649, 84969] C815 ---) [1049, 1298, 81325] C163
38) [3257, 3398, 333113] C815 33) [2753, 1699, 638372] C815
39) [3313, 515, 58852] C815 74) [14713, 1030, 29817] C815
40) [3449, 3518, 1107457] C815 58) [6553, 1759, 496656] C815
41) [3593, 4055, 4102672] C815 55) [5233, 2439, 229952] C815
42) [4013, 1357, 17929] C815 ---) [17929, 2714, 1769733] C2445
43) [4021, 7030, 3090841] C815 82) [18289, 3515, 2316096] C815
44) [4241, 3123, 2411776] C815 62) [9421, 6246, 106025] C815
45) [4297, 2107, 77508] C815 ---) [2153, 2895, 1100032] C5 x C815
46) [4441, 2402, 3517] C815 ---) [3517, 1201, 359721] C163
47) [4801, 5543, 4799412] C815 75) [14813, 8529, 2539729] C815
48) [4813, 2161, 896749] C815 83) [18301, 4322, 1082925] C815
49) [4861, 7257, 273425] C815 65) [10937, 3663, 3286036] C815
50) [4877, 9697, 21653473] C815 78) [15817, 5215, 6320592] C815
51) [4909, 1133, 113517] C815 69) [12613, 2266, 829621] C815
52) [4937, 3962, 2324773] C815 ---) [19213, 1981, 399897] C2445
53) [4957, 6054, 7179929] C815 86) [19889, 3027, 495700] C815
54) [5101, 6737, 1245537] C815 ---) [15377, 5823, 7365844] C10595
55) [5233, 2439, 229952] C815 41) [3593, 4055, 4102672] C815
56) [5693, 8849, 2040337] C815 68) [12073, 5243, 204948] C815
57) [5701, 809, 127989] C815 72) [14221, 1618, 142525] C815
58) [6553, 1759, 496656] C815 40) [3449, 3518, 1107457] C815
59) [6949, 5570, 5504749] C815 ---) [4021, 2785, 562869] C163
60) [6949, 441, 5189] C815 ---) [5189, 882, 173725] C163
61) [9181, 2797, 25497] C815 ---) [2833, 4651, 5288256] C163
62) [9421, 6246, 106025] C815 44) [4241, 3123, 2411776] C815
63) [9433, 595, 86148] C815 32) [2393, 1190, 9433] C815
64) [9829, 2773, 1212237] C815 ---) [797, 2553, 1189309] C163
65) [10937, 3663, 3286036] C815 49) [4861, 7257, 273425] C815
66) [11701, 5317, 3882025] C815 35) [3169, 5047, 1170100] C815
67) [12041, 2099, 424144] C815 ---) [541, 1649, 108369] C163
68) [12073, 5243, 204948] C815 56) [5693, 8849, 2040337] C815
69) [12613, 2266, 829621] C815 51) [4909, 1133, 113517] C815
70) [12637, 1289, 260577] C815 36) [3217, 2578, 619213] C815
71) [13669, 673, 27801] C815 34) [3089, 1346, 341725] C815
72) [14221, 1618, 142525] C815 57) [5701, 809, 127989] C815
73) [14713, 3350, 686953] C815 31) [2377, 1675, 529668] C815
74) [14713, 1030, 29817] C815 39) [3313, 515, 58852] C815
75) [14813, 8529, 2539729] C815 47) [4801, 5543, 4799412] C815
76) [15473, 1610, 586133] C815 ---) [317, 805, 15473] C163
77) [15569, 5347, 5742500] C815 30) [2297, 3823, 249104] C815
78) [15817, 5215, 6320592] C815 50) [4877, 9697, 21653473] C815
79) [16193, 2078, 43169] C815 24) [881, 1039, 259088] C815
80) [17033, 2234, 1179557] C815 ---) [317, 1117, 17033] C163
81) [18253, 1574, 327321] C815 ---) [449, 787, 73012] C163
82) [18289, 3515, 2316096] C815 43) [4021, 7030, 3090841] C815
83) [18301, 4322, 1082925] C815 48) [4813, 2161, 896749] C815
84) [18353, 6675, 2655232] C815 ---) [2593, 3571, 2642832] C163
85) [18773, 2017, 223913] C815 ---) [233, 1967, 300368] C163
86) [19889, 3027, 495700] C815 53) [4957, 6054, 7179929] C815
87) [35509, 1550, 32481] C815 19) [401, 775, 142036] C815
88) [44741, 937, 118825] C815 ---) [97, 1874, 402669] C163
89) [45533, 217, 389] C815 ---) [389, 434, 45533] C163
90) [48497, 1607, 633488] C815 9) [137, 2351, 775952] C815
91) [53437, 313, 11133] C815 ---) [1237, 626, 53437] C163
92) [66713, 1319, 17984] C815 16) [281, 2638, 1667825] C815
93) [120473, 411, 12112] C815 23) [757, 822, 120473] C815
94) [180137, 467, 9488] C815 ---) [593, 934, 180137] C163
95) [232633, 483, 164] C815 5) [41, 966, 232633] C815
96) [286733, 537, 409] C815 20) [409, 1074, 286733] C815
97) [307381, 2490, 320501] C815 25) [1109, 1245, 307381] C815
98) [338033, 615, 10048] C815 12) [157, 1230, 338033] C815
99) [498521, 2139, 1019200] C815 ---) [13, 1689, 498521] C163
100) [504857, 731, 7376] C815 21) [461, 1462, 504857] C815
101) [692917, 3330, 557] C815 22) [557, 1665, 692917] C815
102) [753689, 891, 10048] C815 11) [157, 1782, 753689] C815
103) [1032497, 1255, 135632] C815 13) [173, 2510, 1032497] C815
104) [1159889, 1079, 1088] C815 4) [17, 2158, 1159889] C815
105) [1393681, 2167, 825552] C815 ---) [13, 4181, 1393681] C163
106) [1415753, 1603, 288464] C815 10) [149, 3206, 1415753] C815
107) [1458521, 1243, 21632] C815 ---) [8, 2486, 1458521] C163
108) [1461553, 3947, 606208] C815 ---) [37, 7894, 13153977] C163
109) [1551049, 1507, 180000] C815 ---) [8, 3014, 1551049] C163
110) [1551289, 1249, 2178] C815 ---) [8, 2498, 1551289] C163
111) [1749941, 1325, 1421] C815 ---) [29, 2650, 1749941] C163
112) [2233433, 1627, 103424] C815 8) [101, 3254, 2233433] C815
113) [2502953, 1587, 3904] C815 7) [61, 3174, 2502953] C815
114) [6382529, 2527, 800] C815 2) [8, 5054, 6382529] C815
115) [10231553, 3199, 512] C815 1) [8, 6398, 10231553] C815