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 C231 non-normal (D4) quartic CM field invariants: 139 fields

K Quartic invariants Cl(OK) Igusa invariants Kr Reflex invariants Cl(OKr) Igusa invariants
1) [5, 10046, 25184449] C3 x C231 139) [25184449, 5023, 11520] C3 x C231
2) [5, 5517, 7218721] C3 x C231 135) [7218721, 3439, 1152000] C3 x C231
3) [5, 9214, 21120769] C3 x C231 138) [21120769, 4607, 25920] C3 x C231
4) [53, 3886, 3609041] C3 x C231 123) [3609041, 1943, 41552] C3 x C231
5) [89, 2067, 239332] C3 x C231 86) [59833, 1399, 115344] C3 x C231
6) [181, 4110, 1257521] C3 x C231 119) [1257521, 2055, 741376] C3 x C231
7) [193, 1822, 817569] C3 x C231 94) [90841, 911, 3088] C3 x C231
8) [229, 4102, 1729737] C3 x C231 ---) [192193, 2051, 619216] C7 x C231
9) [257, 1906, 43661] C3 x C231 ---) [43661, 953, 216137] C231
10) [257, 542, 7649] C3 x C231 ---) [7649, 271, 16448] C231
11) [257, 406, 4201] C3 x C231 ---) [4201, 203, 9252] C231
12) [293, 4126, 580577] C3 x C231 110) [580577, 2063, 918848] C3 x C231
13) [293, 1550, 581873] C3 x C231 111) [581873, 775, 4688] C3 x C231
14) [317, 1661, 687749] C3 x C231 ---) [687749, 3322, 7925] C3 x C1155
15) [409, 714, 125813] C3 x C231 96) [125813, 357, 409] C3 x C231
16) [613, 630, 89417] C3 x C231 ---) [89417, 315, 2452] C3 x C3 x C231
17) [733, 1954, 951597] C3 x C231 ---) [105733, 977, 733] C231
18) [761, 2330, 14821] C3 x C231 ---) [14821, 1165, 335601] C231
19) [761, 1843, 428900] C3 x C231 ---) [4289, 1135, 12176] C231
20) [853, 573, 71633] C3 x C231 90) [71633, 1146, 41797] C3 x C231
21) [937, 1878, 821753] C3 x C231 114) [821753, 939, 14992] C3 x C231
22) [1181, 614, 75353] C3 x C231 91) [75353, 307, 4724] C3 x C231
23) [1373, 789, 147049] C3 x C231 ---) [3001, 1578, 34325] C231
24) [1613, 953, 207293] C3 x C231 ---) [207293, 1906, 79037] C3 x C3 x C231
25) [2213, 845, 18617] C3 x C231 ---) [18617, 1690, 639557] C231
26) [2557, 5697, 7499633] C3 x C231 ---) [14177, 3347, 1237588] C231
27) [2677, 5129, 17341] C3 x C231 ---) [17341, 5657, 3279325] C231
28) [2677, 1965, 611273] C3 x C231 ---) [3617, 2619, 42832] C231
29) [2777, 3586, 4637] C3 x C231 ---) [4637, 1793, 802553] C231
30) [2857, 2471, 205812] C3 x C231 ---) [5717, 3957, 482833] C231
31) [2861, 3653, 1887721] C3 x C231 71) [15601, 6675, 183104] C3 x C231
32) [2917, 533, 11953] C3 x C231 ---) [11953, 1066, 236277] C231
33) [2917, 401, 21969] C3 x C231 ---) [2441, 802, 72925] C231
34) [4001, 1922, 139325] C3 x C231 ---) [5573, 961, 196049] C231
35) [4013, 233, 12569] C3 x C231 65) [12569, 466, 4013] C3 x C231
36) [4021, 886, 131913] C3 x C231 70) [14657, 443, 16084] C3 x C231
37) [4649, 1714, 715853] C3 x C231 ---) [2477, 857, 4649] C231
38) [4673, 4074, 4130677] C3 x C231 69) [14293, 2037, 4673] C3 x C231
39) [4933, 1641, 642389] C3 x C231 ---) [5309, 3282, 123325] C231
40) [4933, 3577, 3167901] C3 x C231 ---) [2909, 2797, 1425637] C231
41) [5081, 3798, 3281017] C3 x C231 ---) [11353, 1899, 81296] C231
42) [5237, 3222, 1254649] C3 x C231 63) [10369, 1611, 335168] C3 x C231
43) [5261, 1437, 357097] C3 x C231 ---) [2113, 2874, 636581] C231
44) [5333, 1742, 417329] C3 x C231 ---) [3449, 871, 85328] C231
45) [5333, 205, 9173] C3 x C231 ---) [9173, 410, 5333] C231
46) [5413, 5505, 3774977] C3 x C231 ---) [10457, 5367, 6257428] C3 x C3 x C231
47) [5417, 407, 7556] C3 x C231 ---) [1889, 814, 135425] C3 x C33
48) [5477, 3814, 2234537] C3 x C231 ---) [2657, 1907, 350528] C231
49) [5477, 8170, 14036357] C3 x C231 ---) [10253, 4085, 662717] C231
50) [5741, 962, 208397] C3 x C231 ---) [4253, 481, 5741] C231
51) [6053, 3601, 1170161] C3 x C231 ---) [4049, 3439, 2421200] C231
52) [6053, 3177, 451693] C3 x C231 ---) [3733, 3557, 2669373] C231
53) [6053, 2234, 642389] C3 x C231 ---) [5309, 1117, 151325] C231
54) [6133, 2226, 625469] C3 x C231 ---) [3701, 1113, 153325] C231
55) [6637, 1193, 274509] C3 x C231 ---) [3389, 2386, 325213] C231
56) [6637, 105, 1097] C3 x C231 ---) [1097, 210, 6637] C231
57) [6997, 5042, 6103549] C3 x C231 ---) [3301, 2521, 62973] C231
58) [6997, 1421, 363121] C3 x C231 ---) [3001, 2842, 566757] C231
59) [8069, 5941, 3980453] C3 x C231 ---) [4733, 4889, 976349] C231
60) [9281, 215, 9236] C3 x C231 ---) [2309, 430, 9281] C231
61) [9413, 125, 1553] C3 x C231 ---) [1553, 250, 9413] C231
62) [9749, 305, 1321] C3 x C231 ---) [1321, 610, 87741] C231
63) [10369, 1611, 335168] C3 x C231 42) [5237, 3222, 1254649] C3 x C231
64) [12197, 6913, 601133] C3 x C231 ---) [3557, 3953, 597653] C231
65) [12569, 466, 4013] C3 x C231 35) [4013, 233, 12569] C3 x C231
66) [12577, 8411, 11872512] C3 x C231 ---) [5153, 4935, 6087268] C231
67) [13537, 3719, 3183616] C3 x C231 ---) [3109, 6629, 8460625] C231
68) [13577, 123, 388] C3 x C231 ---) [97, 246, 13577] C231
69) [14293, 2037, 4673] C3 x C231 38) [4673, 4074, 4130677] C3 x C231
70) [14657, 443, 16084] C3 x C231 36) [4021, 886, 131913] C3 x C231
71) [15601, 6675, 183104] C3 x C231 31) [2861, 3653, 1887721] C3 x C231
72) [15661, 1701, 625469] C3 x C231 ---) [3701, 3402, 391525] C231
73) [15733, 3281, 2592909] C3 x C231 ---) [2381, 6341, 1903693] C231
74) [16649, 7918, 9014081] C3 x C231 ---) [3209, 3959, 1664900] C231
75) [16649, 2783, 433700] C3 x C231 ---) [4337, 5566, 6010289] C231
76) [17609, 2071, 539588] C3 x C231 ---) [2753, 4142, 2130689] C231
77) [18521, 967, 118016] C3 x C231 ---) [461, 1934, 463025] C231
78) [18661, 165, 2141] C3 x C231 ---) [2141, 330, 18661] C231
79) [22397, 781, 102097] C3 x C231 ---) [193, 1562, 201573] C231
80) [26029, 1502, 147537] C3 x C231 ---) [97, 751, 104116] C231
81) [32413, 733, 61393] C3 x C231 ---) [73, 1466, 291717] C231
82) [32569, 911, 3924] C3 x C231 ---) [109, 1822, 814225] C231
83) [35129, 1534, 26225] C3 x C231 ---) [1049, 767, 140516] C231
84) [54409, 962, 13725] C3 x C231 ---) [61, 481, 54409] C231
85) [56713, 547, 60624] C3 x C231 ---) [421, 1094, 56713] C231
86) [59833, 1399, 115344] C3 x C231 5) [89, 2067, 239332] C3 x C231
87) [62233, 347, 14544] C3 x C231 ---) [101, 694, 62233] C231
88) [64901, 1098, 41797] C3 x C231 ---) [853, 549, 64901] C231
89) [71429, 269, 233] C3 x C231 ---) [233, 538, 71429] C231
90) [71633, 1146, 41797] C3 x C231 20) [853, 573, 71633] C3 x C231
91) [75353, 307, 4724] C3 x C231 22) [1181, 614, 75353] C3 x C231
92) [79481, 1559, 110864] C3 x C231 ---) [41, 1139, 317924] C231
93) [86113, 431, 24912] C3 x C231 ---) [173, 862, 86113] C231
94) [90841, 911, 3088] C3 x C231 7) [193, 1822, 817569] C3 x C231
95) [113149, 1346, 333] C3 x C231 ---) [37, 673, 113149] C231
96) [125813, 357, 409] C3 x C231 15) [409, 714, 125813] C3 x C231
97) [144757, 381, 101] C3 x C231 ---) [101, 762, 144757] C231
98) [146921, 403, 3872] C3 x C231 ---) [8, 806, 146921] C33
99) [148061, 1610, 55781] C3 x C231 ---) [461, 805, 148061] C231
100) [151817, 1411, 459776] C3 x C231 ---) [449, 2822, 151817] C231
101) [191669, 557, 29645] C3 x C231 ---) [5, 901, 191669] C33
102) [200201, 2275, 1243856] C3 x C231 ---) [269, 4550, 200201] C231
103) [209201, 3271, 112148] C3 x C231 ---) [53, 3101, 209201] C231
104) [222941, 473, 197] C3 x C231 ---) [197, 946, 222941] C231
105) [242681, 715, 67136] C3 x C231 ---) [1049, 1430, 242681] C231
106) [251033, 539, 9872] C3 x C231 ---) [617, 1078, 251033] C231
107) [411449, 651, 3088] C3 x C231 ---) [193, 1302, 411449] C231
108) [507329, 727, 5300] C3 x C231 ---) [53, 1454, 507329] C231
109) [559841, 783, 13312] C3 x C231 ---) [13, 1566, 559841] C231
110) [580577, 2063, 918848] C3 x C231 12) [293, 4126, 580577] C3 x C231
111) [581873, 775, 4688] C3 x C231 13) [293, 1550, 581873] C3 x C231
112) [689789, 833, 1025] C3 x C231 ---) [41, 1666, 689789] C231
113) [814633, 1075, 85248] C3 x C231 ---) [37, 2150, 814633] C231
114) [821753, 939, 14992] C3 x C231 21) [937, 1878, 821753] C3 x C231
115) [899473, 983, 16704] C3 x C231 ---) [29, 1966, 899473] C231
116) [913457, 967, 5408] C3 x C231 ---) [8, 1934, 913457] C231
117) [1046393, 1035, 6208] C3 x C231 ---) [97, 2070, 1046393] C231
118) [1119697, 1687, 431568] C3 x C231 ---) [37, 3374, 1119697] C231
119) [1257521, 2055, 741376] C3 x C231 6) [181, 4110, 1257521] C3 x C231
120) [2022049, 1423, 720] C3 x C231 ---) [5, 2846, 2022049] C231
121) [2178409, 1523, 35280] C3 x C231 ---) [5, 3046, 2178409] C231
122) [3223273, 1811, 14112] C3 x C231 ---) [8, 3622, 3223273] C231
123) [3609041, 1943, 41552] C3 x C231 4) [53, 3886, 3609041] C3 x C231
124) [3960217, 2107, 119808] C3 x C231 ---) [13, 4214, 3960217] C231
125) [4111993, 2699, 793152] C3 x C231 ---) [17, 5398, 4111993] C231
126) [4273849, 2251, 198288] C3 x C231 ---) [17, 4502, 4273849] C231
127) [4661089, 2767, 748800] C3 x C231 ---) [13, 5534, 4661089] C231
128) [4671809, 2783, 768320] C3 x C231 ---) [5, 4429, 4671809] C231
129) [5534489, 3067, 968000] C3 x C231 ---) [5, 4801, 5534489] C231
130) [5543249, 2423, 81920] C3 x C231 ---) [5, 4846, 5543249] C231
131) [5635321, 2443, 83232] C3 x C231 ---) [8, 4886, 5635321] C231
132) [5739229, 2697, 383645] C3 x C231 ---) [5, 5321, 5739229] C231
133) [6263417, 2507, 5408] C3 x C231 ---) [8, 5014, 6263417] C231
134) [6675161, 2587, 4352] C3 x C231 ---) [17, 5174, 6675161] C231
135) [7218721, 3439, 1152000] C3 x C231 2) [5, 5517, 7218721] C3 x C231
136) [7587977, 2755, 512] C3 x C231 ---) [8, 5510, 7587977] C231
137) [11994349, 3777, 567845] C3 x C231 ---) [5, 7554, 11994349] C231
138) [21120769, 4607, 25920] C3 x C231 3) [5, 9214, 21120769] C3 x C231
139) [25184449, 5023, 11520] C3 x C231 1) [5, 10046, 25184449] C3 x C231