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 C849 non-normal (D4) quartic CM field invariants: 149 fields

K Quartic invariants Cl(OK) Igusa invariants Kr Reflex invariants Cl(OKr) Igusa invariants
1) [5, 10526, 27696289] C849 ---) [27696289, 5263, 720] C3 x C21225
2) [8, 4526, 4801169] C849 ---) [4801169, 2263, 80000] C3 x C849
3) [8, 5086, 6351649] C849 144) [6351649, 2543, 28800] C849
4) [8, 5278, 6963169] C849 ---) [6963169, 2639, 288] C3 x C849
5) [13, 10550, 27823753] C849 ---) [27823753, 5275, 468] C4245
6) [29, 5750, 8174681] C849 146) [8174681, 2875, 22736] C849
7) [29, 5878, 8370457] C849 ---) [8370457, 2939, 66816] C3 x C849
8) [29, 4846, 4801873] C849 141) [4801873, 2423, 267264] C849
9) [37, 4494, 5011121] C849 143) [5011121, 2247, 9472] C849
10) [41, 1454, 360593] C849 ---) [360593, 727, 41984] C3 x C849
11) [61, 2382, 1028081] C849 135) [1028081, 1191, 97600] C849
12) [61, 2622, 1656257] C849 138) [1656257, 1311, 15616] C849
13) [73, 1694, 418401] C849 ---) [46489, 847, 74752] C3 x C849
14) [89, 1438, 152417] C849 123) [152417, 719, 91136] C849
15) [101, 2494, 1529153] C849 137) [1529153, 1247, 6464] C849
16) [109, 4646, 4831273] C849 142) [4831273, 2323, 141264] C849
17) [109, 2358, 692441] C849 132) [692441, 1179, 174400] C849
18) [193, 1758, 167393] C849 124) [167393, 879, 151312] C849
19) [229, 1209, 363989] C849 ---) [363989, 2418, 5725] C283
20) [241, 2195, 789444] C849 119) [21929, 1319, 385600] C849
21) [257, 530, 69197] C849 ---) [69197, 265, 257] C283
22) [257, 1303, 362708] C849 ---) [90677, 2606, 246977] C283
23) [257, 3311, 2722112] C849 ---) [42533, 2861, 2035697] C1981
24) [389, 2902, 885497] C849 134) [885497, 1451, 304976] C849
25) [521, 1082, 290597] C849 127) [290597, 541, 521] C849
26) [857, 2711, 289424] C849 115) [18089, 4171, 3428] C849
27) [1097, 539, 72356] C849 116) [18089, 1078, 1097] C849
28) [1097, 342, 11689] C849 91) [11689, 171, 4388] C849
29) [1097, 874, 186581] C849 125) [186581, 437, 1097] C849
30) [1193, 1239, 276112] C849 ---) [17257, 2478, 430673] C5943
31) [1193, 3150, 2175217] C849 113) [17977, 1575, 76352] C849
32) [1481, 1718, 145481] C849 42) [2969, 859, 148100] C849
33) [1609, 1947, 947300] C849 82) [9473, 3894, 1609] C849
34) [1721, 898, 194717] C849 ---) [194717, 449, 1721] C3 x C849
35) [2089, 1739, 187300] C849 ---) [1873, 1727, 33424] C283
36) [2137, 1182, 212513] C849 58) [4337, 591, 34192] C849
37) [2137, 2371, 225252] C849 75) [6257, 2835, 1444612] C849
38) [2417, 2126, 511217] C849 86) [10433, 1063, 154688] C849
39) [2441, 454, 12473] C849 97) [12473, 227, 9764] C849
40) [2741, 2649, 816193] C849 109) [16657, 5298, 3752429] C849
41) [2857, 994, 144157] C849 ---) [853, 497, 25713] C283
42) [2969, 859, 148100] C849 32) [1481, 1718, 145481] C849
43) [3061, 5213, 6315561] C849 98) [14321, 6531, 7652500] C849
44) [3061, 3761, 3260025] C849 101) [14489, 6279, 4897600] C849
45) [3109, 313, 17497] C849 111) [17497, 626, 27981] C849
46) [3217, 1602, 11069] C849 88) [11069, 801, 157633] C849
47) [3257, 1558, 554729] C849 ---) [11321, 779, 13028] C3 x C4245
48) [3313, 1450, 406357] C849 80) [8293, 725, 29817] C849
49) [3361, 4431, 4907600] C849 ---) [12269, 4785, 568009] C3 x C849
50) [3469, 5169, 2307833] C849 118) [19073, 6867, 11669716] C849
51) [3709, 1678, 169825] C849 76) [6793, 839, 133524] C849
52) [3769, 1943, 256912] C849 106) [16057, 3886, 2747601] C849
53) [3793, 1887, 297536] C849 ---) [4649, 3774, 2370625] C3 x C849
54) [3881, 2626, 466525] C849 ---) [18661, 1313, 314361] C3 x C849
55) [4001, 5810, 2661581] C849 ---) [15749, 2905, 1444361] C283
56) [4093, 1265, 104337] C849 90) [11593, 2530, 1182877] C849
57) [4153, 330, 10613] C849 ---) [10613, 165, 4153] C4245
58) [4337, 591, 34192] C849 36) [2137, 1182, 212513] C849
59) [4349, 4289, 1988393] C849 107) [16433, 8578, 10441949] C849
60) [4457, 2755, 24452] C849 ---) [6113, 5510, 7492217] C4245
61) [4733, 3246, 740929] C849 ---) [15121, 1623, 473300] C4245
62) [5009, 6402, 9745501] C849 84) [10141, 3201, 125225] C849
63) [5081, 691, 118100] C849 ---) [1181, 1382, 5081] C283
64) [5113, 9931, 23427792] C849 114) [18077, 7141, 9453937] C849
65) [5197, 3706, 1749781] C849 100) [14461, 1853, 420957] C849
66) [5209, 3842, 168957] C849 ---) [18773, 1921, 880321] C4245
67) [5281, 1191, 353300] C849 ---) [3533, 2382, 5281] C283
68) [5297, 322, 4733] C849 ---) [4733, 161, 5297] C283
69) [5333, 257, 4513] C849 ---) [4513, 514, 47997] C283
70) [5569, 5727, 1181300] C849 93) [11813, 6197, 9361489] C849
71) [5693, 2182, 370489] C849 78) [7561, 1091, 204948] C849
72) [5857, 879, 191696] C849 95) [11981, 1758, 5857] C849
73) [5881, 6955, 4681476] C849 99) [14449, 6175, 7621776] C849
74) [5981, 4141, 397825] C849 105) [15913, 8282, 15556581] C849
75) [6257, 2835, 1444612] C849 37) [2137, 2371, 225252] C849
76) [6793, 839, 133524] C849 51) [3709, 1678, 169825] C849
77) [7481, 291, 19300] C849 ---) [193, 582, 7481] C283
78) [7561, 1091, 204948] C849 71) [5693, 2182, 370489] C849
79) [7673, 1394, 455117] C849 ---) [2693, 697, 7673] C283
80) [8293, 725, 29817] C849 48) [3313, 1450, 406357] C849
81) [9293, 6669, 689821] C849 ---) [5701, 6629, 2090925] C283
82) [9473, 3894, 1609] C849 33) [1609, 1947, 947300] C849
83) [10069, 1717, 533125] C849 ---) [853, 2537, 815589] C283
84) [10141, 3201, 125225] C849 62) [5009, 6402, 9745501] C849
85) [10333, 6333, 2770373] C849 ---) [5237, 4681, 5466157] C283
86) [10433, 1063, 154688] C849 38) [2417, 2126, 511217] C849
87) [10733, 121, 977] C849 ---) [977, 242, 10733] C283
88) [11069, 801, 157633] C849 46) [3217, 1602, 11069] C849
89) [11197, 4401, 136661] C849 ---) [2789, 3629, 3235933] C283
90) [11593, 2530, 1182877] C849 56) [4093, 1265, 104337] C849
91) [11689, 171, 4388] C849 28) [1097, 342, 11689] C849
92) [11777, 1338, 400453] C849 ---) [757, 669, 11777] C283
93) [11813, 6197, 9361489] C849 70) [5569, 5727, 1181300] C849
94) [11821, 7541, 146725] C849 ---) [5869, 7765, 106389] C283
95) [11981, 1758, 5857] C849 72) [5857, 879, 191696] C849
96) [12401, 6599, 813988] C849 ---) [4153, 6303, 2430596] C283
97) [12473, 227, 9764] C849 39) [2441, 454, 12473] C849
98) [14321, 6531, 7652500] C849 43) [3061, 5213, 6315561] C849
99) [14449, 6175, 7621776] C849 73) [5881, 6955, 4681476] C849
100) [14461, 1853, 420957] C849 65) [5197, 3706, 1749781] C849
101) [14489, 6279, 4897600] C849 44) [3061, 3761, 3260025] C849
102) [15349, 9185, 13995981] C849 ---) [5381, 7241, 5540989] C283
103) [15661, 6377, 3584997] C849 ---) [2357, 3257, 2646709] C283
104) [15773, 2514, 2749] C849 ---) [2749, 1257, 394325] C283
105) [15913, 8282, 15556581] C849 74) [5981, 4141, 397825] C849
106) [16057, 3886, 2747601] C849 52) [3769, 1943, 256912] C849
107) [16433, 8578, 10441949] C849 59) [4349, 4289, 1988393] C849
108) [16481, 1634, 74173] C849 ---) [613, 817, 148329] C283
109) [16657, 5298, 3752429] C849 40) [2741, 2649, 816193] C849
110) [16673, 1255, 56128] C849 ---) [877, 2510, 1350513] C283
111) [17497, 626, 27981] C849 45) [3109, 313, 17497] C849
112) [17581, 9450, 22255301] C849 ---) [5981, 4725, 17581] C283
113) [17977, 1575, 76352] C849 31) [1193, 3150, 2175217] C849
114) [18077, 7141, 9453937] C849 64) [5113, 9931, 23427792] C849
115) [18089, 4171, 3428] C849 26) [857, 2711, 289424] C849
116) [18089, 1078, 1097] C849 27) [1097, 539, 72356] C849
117) [18661, 3421, 457893] C849 ---) [5653, 6842, 9871669] C283
118) [19073, 6867, 11669716] C849 50) [3469, 5169, 2307833] C849
119) [21929, 1319, 385600] C849 20) [241, 2195, 789444] C849
120) [29989, 1857, 674681] C849 ---) [281, 2915, 479824] C283
121) [35597, 1985, 264217] C849 ---) [193, 1731, 569552] C283
122) [86501, 1258, 49637] C849 ---) [1013, 629, 86501] C283
123) [152417, 719, 91136] C849 14) [89, 1438, 152417] C849
124) [167393, 879, 151312] C849 18) [193, 1758, 167393] C849
125) [186581, 437, 1097] C849 29) [1097, 874, 186581] C849
126) [190753, 4295, 749008] C849 ---) [277, 7201, 1716777] C283
127) [290597, 541, 521] C849 25) [521, 1082, 290597] C849
128) [315181, 937, 140697] C849 ---) [193, 1874, 315181] C283
129) [338773, 677, 29889] C849 ---) [41, 1354, 338773] C283
130) [446009, 2091, 981568] C849 ---) [313, 4182, 446009] C283
131) [615793, 799, 5652] C849 ---) [157, 1598, 615793] C283
132) [692441, 1179, 174400] C849 17) [109, 2358, 692441] C849
133) [834593, 975, 29008] C849 ---) [37, 1950, 834593] C283
134) [885497, 1451, 304976] C849 24) [389, 2902, 885497] C849
135) [1028081, 1191, 97600] C849 11) [61, 2382, 1028081] C849
136) [1246433, 1295, 107648] C849 ---) [8, 2590, 1246433] C283
137) [1529153, 1247, 6464] C849 15) [101, 2494, 1529153] C849
138) [1656257, 1311, 15616] C849 12) [61, 2622, 1656257] C849
139) [2404009, 1747, 162000] C849 ---) [5, 3441, 2404009] C283
140) [2489857, 4739, 12352] C849 ---) [193, 9478, 22408713] C283
141) [4801873, 2423, 267264] C849 8) [29, 4846, 4801873] C849
142) [4831273, 2323, 141264] C849 16) [109, 4646, 4831273] C849
143) [5011121, 2247, 9472] C849 9) [37, 4494, 5011121] C849
144) [6351649, 2543, 28800] C849 3) [8, 5086, 6351649] C849
145) [7193401, 3307, 935712] C849 ---) [8, 6614, 7193401] C283
146) [8174681, 2875, 22736] C849 6) [29, 5750, 8174681] C849
147) [10165721, 3227, 61952] C849 ---) [8, 6454, 10165721] C283
148) [11114473, 3539, 352512] C849 ---) [17, 7078, 11114473] C283
149) [13212713, 3635, 128] C849 ---) [8, 7270, 13212713] C283