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 C805 non-normal (D4) quartic CM field invariants: 157 fields

K Quartic invariants Cl(OK) Igusa invariants Kr Reflex invariants Cl(OKr) Igusa invariants
1) [8, 5726, 8175137] C805 156) [8175137, 2863, 5408] C805
2) [8, 5662, 8004193] C805 ---) [8004193, 2831, 2592] C37835
3) [8, 5822, 8166593] C805 155) [8166593, 2911, 76832] C805
4) [8, 3406, 2734321] C805 150) [2734321, 1703, 41472] C805
5) [8, 4430, 4680433] C805 154) [4680433, 2215, 56448] C805
6) [13, 5790, 8377697] C805 157) [8377697, 2895, 832] C805
7) [17, 2110, 956353] C805 144) [956353, 1055, 39168] C805
8) [17, 2030, 991057] C805 145) [991057, 1015, 9792] C805
9) [29, 3766, 3478873] C805 ---) [3478873, 1883, 16704] C2415
10) [37, 4422, 4651721] C805 153) [4651721, 2211, 59200] C805
11) [89, 838, 174137] C805 127) [174137, 419, 356] C805
12) [97, 1411, 130852] C805 116) [32713, 1651, 19012] C805
13) [109, 1393, 455437] C805 135) [455437, 2786, 118701] C805
14) [113, 1454, 499601] C805 ---) [499601, 727, 7232] C5 x C4025
15) [157, 2238, 1091393] C805 ---) [1091393, 1119, 40192] C2415
16) [173, 2038, 761561] C805 139) [761561, 1019, 69200] C805
17) [197, 2398, 630689] C805 137) [630689, 1199, 201728] C805
18) [197, 2918, 1321769] C805 147) [1321769, 1459, 201728] C805
19) [269, 2798, 855377] C805 142) [855377, 1399, 275456] C805
20) [677, 1489, 525677] C805 ---) [525677, 2978, 114413] C5 x C805
21) [797, 974, 186161] C805 128) [186161, 487, 12752] C805
22) [829, 861, 160253] C805 126) [160253, 1722, 100309] C805
23) [1093, 233, 11113] C805 ---) [11113, 466, 9837] C161
24) [1093, 709, 46701] C805 ---) [5189, 1418, 315877] C161
25) [1601, 350, 5009] C805 ---) [5009, 175, 6404] C115
26) [1601, 366, 7873] C805 ---) [7873, 183, 6404] C1035
27) [1601, 1599, 638800] C805 ---) [1597, 1521, 577961] C115
28) [1741, 961, 132949] C805 124) [132949, 1922, 391725] C805
29) [1801, 2331, 925700] C805 84) [9257, 4423, 4869904] C805
30) [2029, 1717, 42597] C805 ---) [4733, 2809, 1706389] C115
31) [2081, 427, 40900] C805 ---) [409, 854, 18729] C161
32) [2113, 4879, 2654352] C805 ---) [18433, 4351, 304272] C5 x C805
33) [2153, 2039, 646996] C805 ---) [3301, 1769, 484425] C161
34) [2477, 705, 123637] C805 123) [123637, 1410, 2477] C805
35) [2657, 1858, 767389] C805 ---) [15661, 929, 23913] C2415
36) [2749, 1021, 254425] C805 89) [10177, 2042, 24741] C805
37) [2797, 3509, 476361] C805 76) [5881, 2927, 1611072] C805
38) [2797, 5029, 6316417] C805 109) [17497, 5275, 2192848] C805
39) [2797, 4657, 4358353] C805 95) [12073, 3635, 402768] C805
40) [3041, 4370, 4664749] C805 ---) [16141, 2185, 27369] C2415
41) [3049, 1303, 405396] C805 93) [11261, 2606, 76225] C805
42) [3089, 1087, 257552] C805 103) [16097, 2174, 151361] C805
43) [3181, 1021, 253453] C805 ---) [877, 1549, 155869] C161
44) [3709, 4390, 11161] C805 91) [11161, 2195, 1201716] C805
45) [3733, 5286, 1012649] C805 79) [8369, 2643, 1493200] C805
46) [3769, 4535, 4454656] C805 108) [17401, 9070, 2747601] C805
47) [3821, 5145, 4507609] C805 81) [8521, 5299, 3438900] C805
48) [3833, 2519, 274496] C805 55) [4289, 3299, 2591108] C805
49) [3881, 6099, 1614100] C805 ---) [16141, 6709, 7859025] C2415
50) [3989, 393, 13681] C805 98) [13681, 786, 99725] C805
51) [4013, 3262, 2082289] C805 107) [17209, 1631, 144468] C805
52) [4057, 4707, 3298484] C805 105) [16829, 9053, 20451337] C805
53) [4253, 8245, 909097] C805 112) [18553, 4911, 4355072] C805
54) [4289, 1727, 75476] C805 113) [18869, 3454, 2680625] C805
55) [4289, 3299, 2591108] C805 48) [3833, 2519, 274496] C805
56) [4297, 3434, 43317] C805 59) [4813, 1717, 726193] C805
57) [4297, 4523, 2741364] C805 80) [8461, 4693, 4297] C805
58) [4357, 2873, 2053729] C805 ---) [5689, 5119, 3921300] C161
59) [4813, 1717, 726193] C805 56) [4297, 3434, 43317] C805
60) [4813, 1517, 140949] C805 ---) [15661, 3034, 1737493] C2415
61) [5209, 5559, 7255508] C805 ---) [10733, 6029, 7131121] C2415
62) [5233, 5419, 7329616] C805 85) [9349, 5297, 3814857] C805
63) [5273, 2438, 136073] C805 ---) [2777, 1219, 337472] C345
64) [5273, 1990, 652553] C805 ---) [5393, 995, 84368] C115
65) [5417, 1331, 376532] C805 ---) [557, 1237, 265433] C115
66) [5417, 1355, 457652] C805 ---) [677, 2005, 915473] C115
67) [5437, 4405, 3860113] C805 77) [7297, 4759, 3675412] C805
68) [5557, 2917, 14173] C805 99) [14173, 5834, 8452197] C805
69) [5557, 3793, 2583949] C805 82) [8941, 6553, 3473125] C805
70) [5557, 7854, 6530129] C805 110) [18089, 3927, 2222800] C805
71) [5573, 2025, 522193] C805 90) [10657, 4050, 2011853] C805
72) [5669, 5441, 4780625] C805 78) [7649, 4051, 566900] C805
73) [5701, 3086, 100449] C805 92) [11161, 1543, 570100] C805
74) [5701, 9069, 378725] C805 102) [15149, 6501, 3563125] C805
75) [5813, 5486, 4175761] C805 100) [14449, 2743, 837072] C805
76) [5881, 2927, 1611072] C805 37) [2797, 3509, 476361] C805
77) [7297, 4759, 3675412] C805 67) [5437, 4405, 3860113] C805
78) [7649, 4051, 566900] C805 72) [5669, 5441, 4780625] C805
79) [8369, 2643, 1493200] C805 45) [3733, 5286, 1012649] C805
80) [8461, 4693, 4297] C805 57) [4297, 4523, 2741364] C805
81) [8521, 5299, 3438900] C805 47) [3821, 5145, 4507609] C805
82) [8941, 6553, 3473125] C805 69) [5557, 3793, 2583949] C805
83) [9029, 766, 2225] C805 ---) [89, 383, 36116] C115
84) [9257, 4423, 4869904] C805 29) [1801, 2331, 925700] C805
85) [9349, 5297, 3814857] C805 62) [5233, 5419, 7329616] C805
86) [9829, 2906, 184725] C805 ---) [821, 1453, 481621] C161
87) [9829, 4194, 4358093] C805 ---) [2357, 2097, 9829] C161
88) [9829, 3365, 2120661] C805 ---) [2909, 4265, 1661101] C161
89) [10177, 2042, 24741] C805 36) [2749, 1021, 254425] C805
90) [10657, 4050, 2011853] C805 71) [5573, 2025, 522193] C805
91) [11161, 2195, 1201716] C805 44) [3709, 4390, 11161] C805
92) [11161, 1543, 570100] C805 73) [5701, 3086, 100449] C805
93) [11261, 2606, 76225] C805 41) [3049, 1303, 405396] C805
94) [11621, 773, 7025] C805 ---) [281, 1546, 569429] C115
95) [12073, 3635, 402768] C805 39) [2797, 4657, 4358353] C805
96) [12301, 901, 175273] C805 ---) [73, 931, 196816] C161
97) [12497, 587, 8036] C805 ---) [41, 539, 49988] C115
98) [13681, 786, 99725] C805 50) [3989, 393, 13681] C805
99) [14173, 5834, 8452197] C805 68) [5557, 2917, 14173] C805
100) [14449, 2743, 837072] C805 75) [5813, 5486, 4175761] C805
101) [15121, 6823, 203076] C805 ---) [5641, 9175, 4899204] C161
102) [15149, 6501, 3563125] C805 74) [5701, 9069, 378725] C805
103) [16097, 2174, 151361] C805 42) [3089, 1087, 257552] C805
104) [16741, 4577, 4529925] C805 ---) [2237, 4757, 820309] C161
105) [16829, 9053, 20451337] C805 52) [4057, 4707, 3298484] C805
106) [16901, 1021, 53573] C805 ---) [317, 2042, 828149] C115
107) [17209, 1631, 144468] C805 51) [4013, 3262, 2082289] C805
108) [17401, 9070, 2747601] C805 46) [3769, 4535, 4454656] C805
109) [17497, 5275, 2192848] C805 38) [2797, 5029, 6316417] C805
110) [18089, 3927, 2222800] C805 70) [5557, 7854, 6530129] C805
111) [18253, 6905, 4979053] C805 ---) [3637, 5713, 8049573] C161
112) [18553, 4911, 4355072] C805 53) [4253, 8245, 909097] C805
113) [18869, 3454, 2680625] C805 54) [4289, 1727, 75476] C805
114) [19081, 743, 18756] C805 ---) [521, 1486, 477025] C115
115) [30893, 1130, 195653] C805 ---) [677, 565, 30893] C161
116) [32713, 1651, 19012] C805 12) [97, 1411, 130852] C805
117) [41777, 818, 173] C805 ---) [173, 409, 41777] C161
118) [71849, 1343, 1856] C805 ---) [29, 965, 71849] C115
119) [94561, 319, 1800] C805 ---) [8, 638, 94561] C115
120) [111029, 1658, 243125] C805 ---) [389, 829, 111029] C161
121) [116437, 1378, 8973] C805 ---) [997, 689, 116437] C161
122) [116437, 1738, 289413] C805 ---) [397, 869, 116437] C161
123) [123637, 1410, 2477] C805 34) [2477, 705, 123637] C805
124) [132949, 1922, 391725] C805 28) [1741, 961, 132949] C805
125) [159437, 1698, 83053] C805 ---) [157, 849, 159437] C161
126) [160253, 1722, 100309] C805 22) [829, 861, 160253] C805
127) [174137, 419, 356] C805 11) [89, 838, 174137] C805
128) [186161, 487, 12752] C805 21) [797, 974, 186161] C805
129) [195697, 487, 10368] C805 ---) [8, 974, 195697] C161
130) [217397, 1874, 8381] C805 ---) [29, 937, 217397] C115
131) [245473, 4282, 3601989] C805 ---) [61, 2141, 245473] C161
132) [277793, 2031, 961792] C805 ---) [13, 1125, 277793] C161
133) [295853, 601, 16337] C805 ---) [17, 1202, 295853] C115
134) [328121, 587, 4112] C805 ---) [257, 1174, 328121] C483
135) [455437, 2786, 118701] C805 13) [109, 1393, 455437] C805
136) [496381, 745, 14661] C805 ---) [181, 1490, 496381] C161
137) [630689, 1199, 201728] C805 17) [197, 2398, 630689] C805
138) [676289, 983, 72500] C805 ---) [29, 1966, 676289] C161
139) [761561, 1019, 69200] C805 16) [173, 2038, 761561] C805
140) [807509, 949, 23273] C805 ---) [17, 1898, 807509] C161
141) [824081, 919, 5120] C805 ---) [5, 1838, 824081] C115
142) [855377, 1399, 275456] C805 19) [269, 2798, 855377] C805
143) [876769, 967, 14580] C805 ---) [5, 1934, 876769] C161
144) [956353, 1055, 39168] C805 7) [17, 2110, 956353] C805
145) [991057, 1015, 9792] C805 8) [17, 2030, 991057] C805
146) [1186489, 1387, 184320] C805 ---) [5, 2241, 1186489] C161
147) [1321769, 1459, 201728] C805 18) [197, 2918, 1321769] C805
148) [1888841, 1379, 3200] C805 ---) [8, 2758, 1888841] C115
149) [2437577, 1955, 346112] C805 ---) [8, 3910, 2437577] C161
150) [2734321, 1703, 41472] C805 4) [8, 3406, 2734321] C805
151) [3169721, 2497, 766322] C805 ---) [8, 4994, 3169721] C115
152) [3953849, 2027, 38720] C805 ---) [5, 4054, 3953849] C161
153) [4651721, 2211, 59200] C805 10) [37, 4422, 4651721] C805
154) [4680433, 2215, 56448] C805 5) [8, 4430, 4680433] C805
155) [8166593, 2911, 76832] C805 3) [8, 5822, 8166593] C805
156) [8175137, 2863, 5408] C805 1) [8, 5726, 8175137] C805
157) [8377697, 2895, 832] C805 6) [13, 5790, 8377697] C805