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 C813 non-normal (D4) quartic CM field invariants: 150 fields

K Quartic invariants Cl(OK) Igusa invariants Kr Reflex invariants Cl(OKr) Igusa invariants
1) [8, 5470, 7469857] C813 147) [7469857, 2735, 2592] C813
2) [8, 4270, 4263313] C813 146) [4263313, 2135, 73728] C813
3) [8, 5822, 8308033] C813 148) [8308033, 2911, 41472] C813
4) [13, 4222, 3849793] C813 145) [3849793, 2111, 151632] C813
5) [13, 3118, 1823953] C813 137) [1823953, 1559, 151632] C813
6) [17, 2990, 2165393] C813 138) [2165393, 1495, 17408] C813
7) [29, 3494, 3050153] C813 141) [3050153, 1747, 464] C813
8) [73, 4318, 4194081] C813 129) [466009, 2159, 116800] C813
9) [97, 1222, 24121] C813 118) [24121, 611, 87300] C813
10) [101, 3158, 1226297] C813 134) [1226297, 1579, 316736] C813
11) [157, 3854, 3622897] C813 144) [3622897, 1927, 22608] C813
12) [173, 2894, 1817009] C813 136) [1817009, 1447, 69200] C813
13) [173, 2846, 1847777] C813 ---) [1847777, 1423, 44288] C5691
14) [181, 2209, 1102225] C813 121) [44089, 2063, 788436] C813
15) [229, 4894, 5621409] C813 ---) [624601, 2447, 91600] C271
16) [233, 1634, 666557] C813 130) [666557, 817, 233] C813
17) [241, 4086, 3418073] C813 142) [3418073, 2043, 188944] C813
18) [257, 539, 18596] C813 58) [4649, 1078, 216137] C813
19) [257, 1238, 366713] C813 ---) [366713, 619, 4112] C271
20) [257, 1342, 413233] C813 ---) [413233, 671, 9252] C271
21) [293, 3502, 797009] C813 ---) [797009, 1751, 567248] C4065
22) [313, 902, 158329] C813 123) [158329, 451, 11268] C813
23) [449, 1106, 304013] C813 127) [304013, 553, 449] C813
24) [617, 2622, 731521] C813 102) [14929, 1311, 246800] C813
25) [641, 938, 155861] C813 ---) [155861, 469, 16025] C3 x C813
26) [757, 1038, 257249] C813 125) [257249, 519, 3028] C813
27) [1097, 915, 64228] C813 107) [16057, 1830, 580313] C813
28) [1229, 377, 20477] C813 ---) [20477, 754, 60221] C271
29) [1249, 342, 9257] C813 83) [9257, 171, 4996] C813
30) [1489, 1067, 13252] C813 ---) [3313, 2134, 1085481] C271
31) [1901, 2201, 70025] C813 ---) [2801, 1331, 190100] C271
32) [2141, 4465, 2859649] C813 111) [16921, 5223, 6714176] C813
33) [2269, 2669, 1685025] C813 76) [7489, 3395, 1306944] C813
34) [2293, 5093, 5218353] C813 89) [11833, 4955, 5283072] C813
35) [2341, 5798, 3872025] C813 114) [17209, 2899, 1133044] C813
36) [2473, 2790, 7193] C813 74) [7193, 1395, 484708] C813
37) [2777, 307, 22868] C813 ---) [5717, 614, 2777] C271
38) [2789, 353, 13721] C813 97) [13721, 706, 69725] C813
39) [2917, 4337, 3704049] C813 62) [5081, 2207, 291700] C813
40) [3049, 5074, 2911725] C813 96) [12941, 2537, 881161] C813
41) [3109, 4238, 3694257] C813 77) [8377, 2119, 198976] C813
42) [3109, 2926, 1692673] C813 72) [5857, 1463, 111924] C813
43) [3301, 1469, 102933] C813 86) [11437, 2938, 1746229] C813
44) [3413, 2021, 829129] C813 112) [16921, 4042, 767925] C813
45) [3457, 6311, 9417024] C813 108) [16349, 5997, 8300257] C813
46) [3469, 3041, 1478493] C813 ---) [18253, 6082, 3333709] C4065
47) [3541, 1402, 363925] C813 100) [14557, 701, 31869] C813
48) [3557, 2222, 722113] C813 101) [14737, 1111, 128052] C813
49) [3733, 2041, 361081] C813 75) [7369, 4082, 2721357] C813
50) [3833, 5706, 2604757] C813 82) [9013, 2853, 1383713] C813
51) [4001, 2623, 1190900] C813 ---) [11909, 5246, 2116529] C271
52) [4021, 2437, 390025] C813 103) [15601, 4874, 4378869] C813
53) [4057, 8523, 12755444] C813 117) [18869, 7577, 12272425] C813
54) [4261, 3365, 1040121] C813 95) [12841, 6730, 7162741] C813
55) [4261, 3773, 3251025] C813 99) [14449, 7546, 1231429] C813
56) [4493, 521, 12821] C813 94) [12821, 1042, 220157] C813
57) [4621, 2145, 816389] C813 ---) [16661, 4290, 1335469] C3 x C813
58) [4649, 1078, 216137] C813 18) [257, 539, 18596] C813
59) [4813, 6766, 10212561] C813 ---) [14009, 3383, 308032] C8943
60) [4933, 850, 3037] C813 ---) [3037, 425, 44397] C271
61) [5009, 2446, 213425] C813 78) [8537, 1223, 320576] C813
62) [5081, 2207, 291700] C813 39) [2917, 4337, 3704049] C813
63) [5189, 9518, 3967681] C813 98) [13729, 4759, 4670100] C813
64) [5189, 1457, 498281] C813 85) [10169, 2914, 129725] C813
65) [5281, 2183, 1190052] C813 ---) [3673, 4366, 5281] C271
66) [5477, 2417, 966173] C813 ---) [5717, 4834, 1977197] C271
67) [5569, 9095, 3525844] C813 ---) [17989, 5789, 3480625] C3 x C2439
68) [5573, 9629, 6013177] C813 110) [16657, 8075, 1805652] C813
69) [5573, 6317, 835009] C813 113) [17041, 9663, 13932500] C813
70) [5581, 453, 16421] C813 109) [16421, 906, 139525] C813
71) [5857, 5486, 4150417] C813 87) [11497, 2743, 843408] C813
72) [5857, 1463, 111924] C813 42) [3109, 2926, 1692673] C813
73) [5881, 5914, 3450949] C813 90) [11941, 2957, 1323225] C813
74) [7193, 1395, 484708] C813 36) [2473, 2790, 7193] C813
75) [7369, 4082, 2721357] C813 49) [3733, 2041, 361081] C813
76) [7489, 3395, 1306944] C813 33) [2269, 2669, 1685025] C813
77) [8377, 2119, 198976] C813 41) [3109, 4238, 3694257] C813
78) [8537, 1223, 320576] C813 61) [5009, 2446, 213425] C813
79) [8597, 2562, 1606573] C813 ---) [3037, 1281, 8597] C271
80) [8597, 661, 3917] C813 ---) [3917, 1322, 421253] C271
81) [8713, 1047, 10484] C813 ---) [2621, 2094, 1054273] C271
82) [9013, 2853, 1383713] C813 50) [3833, 5706, 2604757] C813
83) [9257, 171, 4996] C813 29) [1249, 342, 9257] C813
84) [9833, 410, 2693] C813 ---) [2693, 205, 9833] C271
85) [10169, 2914, 129725] C813 64) [5189, 1457, 498281] C813
86) [11437, 2938, 1746229] C813 43) [3301, 1469, 102933] C813
87) [11497, 2743, 843408] C813 71) [5857, 5486, 4150417] C813
88) [11789, 4341, 1100689] C813 ---) [3049, 4871, 424404] C271
89) [11833, 4955, 5283072] C813 34) [2293, 5093, 5218353] C813
90) [11941, 2957, 1323225] C813 73) [5881, 5914, 3450949] C813
91) [12197, 5381, 502997] C813 ---) [4157, 7289, 12197] C271
92) [12269, 1969, 966173] C813 ---) [5717, 3938, 12269] C271
93) [12577, 4147, 447696] C813 ---) [3109, 5773, 1018737] C271
94) [12821, 1042, 220157] C813 56) [4493, 521, 12821] C813
95) [12841, 6730, 7162741] C813 54) [4261, 3365, 1040121] C813
96) [12941, 2537, 881161] C813 40) [3049, 5074, 2911725] C813
97) [13721, 706, 69725] C813 38) [2789, 353, 13721] C813
98) [13729, 4759, 4670100] C813 63) [5189, 9518, 3967681] C813
99) [14449, 7546, 1231429] C813 55) [4261, 3773, 3251025] C813
100) [14557, 701, 31869] C813 47) [3541, 1402, 363925] C813
101) [14737, 1111, 128052] C813 48) [3557, 2222, 722113] C813
102) [14929, 1311, 246800] C813 24) [617, 2622, 731521] C813
103) [15601, 4874, 4378869] C813 52) [4021, 2437, 390025] C813
104) [15737, 1339, 129556] C813 ---) [661, 2678, 1274697] C271
105) [15773, 2161, 27881] C813 ---) [569, 2083, 1009472] C271
106) [15773, 514, 2957] C813 ---) [2957, 257, 15773] C271
107) [16057, 1830, 580313] C813 27) [1097, 915, 64228] C813
108) [16349, 5997, 8300257] C813 45) [3457, 6311, 9417024] C813
109) [16421, 906, 139525] C813 70) [5581, 453, 16421] C813
110) [16657, 8075, 1805652] C813 68) [5573, 9629, 6013177] C813
111) [16921, 5223, 6714176] C813 32) [2141, 4465, 2859649] C813
112) [16921, 4042, 767925] C813 44) [3413, 2021, 829129] C813
113) [17041, 9663, 13932500] C813 69) [5573, 6317, 835009] C813
114) [17209, 2899, 1133044] C813 35) [2341, 5798, 3872025] C813
115) [18097, 7559, 11456964] C813 ---) [3929, 6423, 3547012] C271
116) [18257, 4902, 1333609] C813 ---) [2521, 2451, 1168448] C271
117) [18869, 7577, 12272425] C813 53) [4057, 8523, 12755444] C813
118) [24121, 611, 87300] C813 9) [97, 1222, 24121] C813
119) [41057, 463, 43328] C813 ---) [677, 926, 41057] C271
120) [41057, 1130, 154997] C813 ---) [293, 565, 41057] C271
121) [44089, 2063, 788436] C813 14) [181, 2209, 1102225] C813
122) [74933, 389, 19097] C813 ---) [113, 778, 74933] C271
123) [158329, 451, 11268] C813 22) [313, 902, 158329] C813
124) [225221, 477, 577] C813 ---) [577, 954, 225221] C5691
125) [257249, 519, 3028] C813 26) [757, 1038, 257249] C813
126) [298349, 2226, 45373] C813 ---) [157, 1113, 298349] C271
127) [304013, 553, 449] C813 23) [449, 1106, 304013] C813
128) [371897, 643, 10388] C813 ---) [53, 1286, 371897] C271
129) [466009, 2159, 116800] C813 8) [73, 4318, 4194081] C813
130) [666557, 817, 233] C813 16) [233, 1634, 666557] C813
131) [783077, 3546, 11221] C813 ---) [229, 1773, 783077] C3 x C813
132) [788549, 893, 2225] C813 ---) [89, 1786, 788549] C271
133) [979949, 993, 1525] C813 ---) [61, 1986, 979949] C271
134) [1226297, 1579, 316736] C813 10) [101, 3158, 1226297] C813
135) [1631057, 1445, 114242] C813 ---) [8, 2890, 1631057] C271
136) [1817009, 1447, 69200] C813 12) [173, 2894, 1817009] C813
137) [1823953, 1559, 151632] C813 5) [13, 3118, 1823953] C813
138) [2165393, 1495, 17408] C813 6) [17, 2990, 2165393] C813
139) [2257609, 2851, 1467648] C813 ---) [13, 5153, 2257609] C271
140) [2851481, 1691, 2000] C813 ---) [5, 3382, 2851481] C271
141) [3050153, 1747, 464] C813 7) [29, 3494, 3050153] C813
142) [3418073, 2043, 188944] C813 17) [241, 4086, 3418073] C813
143) [3609889, 1903, 2880] C813 ---) [5, 3806, 3609889] C271
144) [3622897, 1927, 22608] C813 11) [157, 3854, 3622897] C813
145) [3849793, 2111, 151632] C813 4) [13, 4222, 3849793] C813
146) [4263313, 2135, 73728] C813 2) [8, 4270, 4263313] C813
147) [7469857, 2735, 2592] C813 1) [8, 5470, 7469857] C813
148) [8308033, 2911, 41472] C813 3) [8, 5822, 8308033] C813
149) [9076009, 3251, 373248] C813 ---) [8, 6502, 9076009] C271
150) [9791321, 3163, 53312] C813 ---) [17, 6326, 9791321] C271