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 C703 non-normal (D4) quartic CM field invariants: 161 fields

K Quartic invariants Cl(OK) Igusa invariants Kr Reflex invariants Cl(OKr) Igusa invariants
1) [5, 9326, 21639889] C703 161) [21639889, 4663, 25920] C703
2) [5, 7582, 14345761] C703 157) [14345761, 3791, 6480] C703
3) [5, 6982, 11899081] C703 ---) [11899081, 3491, 72000] C21793
4) [5, 9526, 21416089] C703 160) [21416089, 4763, 317520] C703
5) [5, 6038, 8466361] C703 151) [8466361, 3019, 162000] C703
6) [8, 7942, 15717641] C703 158) [15717641, 3971, 12800] C703
7) [8, 6670, 9370033] C703 153) [9370033, 3335, 438048] C703
8) [8, 6782, 10319233] C703 155) [10319233, 3391, 294912] C703
9) [13, 5430, 7330457] C703 150) [7330457, 2715, 10192] C703
10) [17, 3022, 1169009] C703 140) [1169009, 1511, 278528] C703
11) [17, 4451, 4283012] C703 139) [1070753, 2351, 1114112] C703
12) [17, 9686, 22661497] C703 ---) [22661497, 4843, 198288] C21793
13) [17, 1750, 351913] C703 127) [351913, 875, 103428] C703
14) [17, 2254, 476977] C703 130) [476977, 1127, 198288] C703
15) [29, 6470, 8564681] C703 152) [8564681, 3235, 475136] C703
16) [29, 4550, 3154441] C703 144) [3154441, 2275, 505296] C703
17) [29, 4406, 2447833] C703 ---) [2447833, 2203, 601344] C3515
18) [41, 2899, 1005028] C703 124) [251257, 2967, 630416] C703
19) [53, 6958, 3623441] C703 146) [3623441, 3479, 2120000] C703
20) [53, 4174, 3690737] C703 ---) [3690737, 2087, 166208] C2109
21) [53, 2086, 813097] C703 135) [813097, 1043, 68688] C703
22) [73, 2658, 1716893] C703 142) [1716893, 1329, 12337] C703
23) [89, 2162, 1065677] C703 138) [1065677, 1081, 25721] C703
24) [97, 6246, 5556521] C703 149) [5556521, 3123, 1049152] C703
25) [97, 6390, 10183193] C703 154) [10183193, 3195, 6208] C703
26) [97, 1022, 161793] C703 114) [17977, 511, 24832] C703
27) [101, 3470, 3003761] C703 143) [3003761, 1735, 1616] C703
28) [101, 3478, 1369337] C703 ---) [1369337, 1739, 413696] C14763
29) [137, 5446, 4573897] C703 148) [4573897, 2723, 710208] C703
30) [137, 6566, 10743017] C703 156) [10743017, 3283, 8768] C703
31) [157, 3870, 840353] C703 136) [840353, 1935, 725968] C703
32) [193, 8246, 16887961] C703 159) [16887961, 4123, 27792] C703
33) [197, 2018, 954253] C703 137) [954253, 1009, 15957] C703
34) [197, 1886, 775777] C703 134) [775777, 943, 28368] C703
35) [233, 4006, 3475177] C703 145) [3475177, 2003, 134208] C703
36) [277, 6166, 4381497] C703 131) [486833, 3083, 1280848] C703
37) [281, 1003, 133412] C703 117) [33353, 2006, 472361] C703
38) [317, 2182, 459913] C703 129) [459913, 1091, 182592] C703
39) [433, 6902, 9664729] C703 ---) [9664729, 3451, 561168] C2109
40) [541, 5862, 6374825] C703 ---) [254993, 2931, 553984] C2109
41) [677, 1810, 686333] C703 133) [686333, 905, 33173] C703
42) [773, 1930, 557093] C703 132) [557093, 965, 93533] C703
43) [877, 2186, 1163077] C703 ---) [1163077, 1093, 7893] C20387
44) [1013, 1238, 123833] C703 120) [123833, 619, 64832] C703
45) [1061, 1298, 416957] C703 128) [416957, 649, 1061] C703
46) [1069, 741, 104933] C703 119) [104933, 1482, 129349] C703
47) [1097, 2438, 1415753] C703 141) [1415753, 1219, 17552] C703
48) [1117, 894, 128321] C703 121) [128321, 447, 17872] C703
49) [1549, 385, 5689] C703 91) [5689, 770, 125469] C703
50) [1549, 1386, 325349] C703 126) [325349, 693, 38725] C703
51) [1613, 1130, 312773] C703 125) [312773, 565, 1613] C703
52) [1721, 374, 7433] C703 93) [7433, 187, 6884] C703
53) [1861, 2422, 1347417] C703 122) [149713, 1211, 29776] C703
54) [2221, 1873, 752101] C703 ---) [15349, 3746, 499725] C2109
55) [2377, 6095, 296848] C703 115) [18553, 4823, 2434048] C703
56) [2381, 1350, 417529] C703 96) [8521, 675, 9524] C703
57) [2549, 4629, 4744513] C703 110) [16417, 4551, 1233716] C703
58) [2729, 1274, 307525] C703 ---) [12301, 637, 24561] C3515
59) [2729, 923, 59476] C703 105) [14869, 1846, 614025] C703
60) [2729, 1702, 331225] C703 101) [13249, 851, 98244] C703
61) [2909, 5769, 7935625] C703 99) [12697, 5179, 6702336] C703
62) [2909, 910, 160481] C703 123) [160481, 455, 11636] C703
63) [3037, 761, 107577] C703 97) [11953, 1522, 148813] C703
64) [3169, 4703, 5110452] C703 ---) [15773, 6153, 7000321] C2109
65) [3413, 5413, 2000009] C703 111) [16529, 5911, 8532500] C703
66) [3541, 6238, 153297] C703 ---) [17033, 3119, 2393716] C3515
67) [3613, 1853, 705753] C703 ---) [8713, 3706, 610597] C2109
68) [3709, 5581, 5909209] C703 ---) [16369, 7075, 12477076] C2109
69) [3821, 2973, 443425] C703 ---) [17737, 5946, 7065029] C10545
70) [3881, 7930, 14960549] C703 113) [17789, 3965, 190169] C703
71) [3917, 2846, 1962257] C703 ---) [16217, 1423, 15668] C4921
72) [4057, 3738, 3087461] C703 ---) [18269, 1869, 101425] C2109
73) [4093, 761, 143757] C703 106) [15973, 1522, 4093] C703
74) [4253, 4009, 801689] C703 109) [16361, 8018, 12865325] C703
75) [4637, 6814, 6859361] C703 116) [19001, 3407, 1187072] C703
76) [4721, 2907, 496900] C703 80) [4969, 4335, 1208576] C703
77) [4721, 1491, 129700] C703 ---) [1297, 2199, 1208576] C7733
78) [4793, 1558, 530153] C703 ---) [3137, 779, 19172] C6327
79) [4957, 6393, 8134433] C703 ---) [15377, 8475, 7157908] C9139
80) [4969, 4335, 1208576] C703 76) [4721, 2907, 496900] C703
81) [5009, 2667, 63892] C703 107) [15973, 5334, 6857321] C703
82) [5009, 7923, 5323600] C703 102) [13309, 5697, 125225] C703
83) [5113, 3503, 479296] C703 94) [7489, 5771, 3456388] C703
84) [5153, 9019, 3298484] C703 112) [16829, 6949, 6312425] C703
85) [5189, 7493, 4217377] C703 104) [14593, 5463, 1328384] C703
86) [5197, 4174, 1362097] C703 ---) [11257, 2087, 748368] C11951
87) [5309, 7878, 15430777] C703 108) [16057, 3939, 21236] C703
88) [5393, 2162, 974413] C703 95) [8053, 1081, 48537] C703
89) [5393, 370, 12653] C703 98) [12653, 185, 5393] C703
90) [5437, 926, 127377] C703 103) [14153, 463, 21748] C703
91) [5689, 770, 125469] C703 49) [1549, 385, 5689] C703
92) [5849, 3283, 1289300] C703 100) [12893, 6566, 5620889] C703
93) [7433, 187, 6884] C703 52) [1721, 374, 7433] C703
94) [7489, 5771, 3456388] C703 83) [5113, 3503, 479296] C703
95) [8053, 1081, 48537] C703 88) [5393, 2162, 974413] C703
96) [8521, 675, 9524] C703 56) [2381, 1350, 417529] C703
97) [11953, 1522, 148813] C703 63) [3037, 761, 107577] C703
98) [12653, 185, 5393] C703 89) [5393, 370, 12653] C703
99) [12697, 5179, 6702336] C703 61) [2909, 5769, 7935625] C703
100) [12893, 6566, 5620889] C703 92) [5849, 3283, 1289300] C703
101) [13249, 851, 98244] C703 60) [2729, 1702, 331225] C703
102) [13309, 5697, 125225] C703 82) [5009, 7923, 5323600] C703
103) [14153, 463, 21748] C703 90) [5437, 926, 127377] C703
104) [14593, 5463, 1328384] C703 85) [5189, 7493, 4217377] C703
105) [14869, 1846, 614025] C703 59) [2729, 923, 59476] C703
106) [15973, 1522, 4093] C703 73) [4093, 761, 143757] C703
107) [15973, 5334, 6857321] C703 81) [5009, 2667, 63892] C703
108) [16057, 3939, 21236] C703 87) [5309, 7878, 15430777] C703
109) [16361, 8018, 12865325] C703 74) [4253, 4009, 801689] C703
110) [16417, 4551, 1233716] C703 57) [2549, 4629, 4744513] C703
111) [16529, 5911, 8532500] C703 65) [3413, 5413, 2000009] C703
112) [16829, 6949, 6312425] C703 84) [5153, 9019, 3298484] C703
113) [17789, 3965, 190169] C703 70) [3881, 7930, 14960549] C703
114) [17977, 511, 24832] C703 26) [97, 1022, 161793] C703
115) [18553, 4823, 2434048] C703 55) [2377, 6095, 296848] C703
116) [19001, 3407, 1187072] C703 75) [4637, 6814, 6859361] C703
117) [33353, 2006, 472361] C703 37) [281, 1003, 133412] C703
118) [70229, 477, 39325] C703 ---) [13, 954, 70229] C37
119) [104933, 1482, 129349] C703 46) [1069, 741, 104933] C703
120) [123833, 619, 64832] C703 44) [1013, 1238, 123833] C703
121) [128321, 447, 17872] C703 48) [1117, 894, 128321] C703
122) [149713, 1211, 29776] C703 53) [1861, 2422, 1347417] C703
123) [160481, 455, 11636] C703 62) [2909, 910, 160481] C703
124) [251257, 2967, 630416] C703 18) [41, 2899, 1005028] C703
125) [312773, 565, 1613] C703 51) [1613, 1130, 312773] C703
126) [325349, 693, 38725] C703 50) [1549, 1386, 325349] C703
127) [351913, 875, 103428] C703 13) [17, 1750, 351913] C703
128) [416957, 649, 1061] C703 45) [1061, 1298, 416957] C703
129) [459913, 1091, 182592] C703 38) [317, 2182, 459913] C703
130) [476977, 1127, 198288] C703 14) [17, 2254, 476977] C703
131) [486833, 3083, 1280848] C703 36) [277, 6166, 4381497] C703
132) [557093, 965, 93533] C703 42) [773, 1930, 557093] C703
133) [686333, 905, 33173] C703 41) [677, 1810, 686333] C703
134) [775777, 943, 28368] C703 34) [197, 1886, 775777] C703
135) [813097, 1043, 68688] C703 21) [53, 2086, 813097] C703
136) [840353, 1935, 725968] C703 31) [157, 3870, 840353] C703
137) [954253, 1009, 15957] C703 33) [197, 2018, 954253] C703
138) [1065677, 1081, 25721] C703 23) [89, 2162, 1065677] C703
139) [1070753, 2351, 1114112] C703 11) [17, 4451, 4283012] C703
140) [1169009, 1511, 278528] C703 10) [17, 3022, 1169009] C703
141) [1415753, 1219, 17552] C703 47) [1097, 2438, 1415753] C703
142) [1716893, 1329, 12337] C703 22) [73, 2658, 1716893] C703
143) [3003761, 1735, 1616] C703 27) [101, 3470, 3003761] C703
144) [3154441, 2275, 505296] C703 16) [29, 4550, 3154441] C703
145) [3475177, 2003, 134208] C703 35) [233, 4006, 3475177] C703
146) [3623441, 3479, 2120000] C703 19) [53, 6958, 3623441] C703
147) [4124777, 2035, 4112] C703 ---) [257, 4070, 4124777] C2109
148) [4573897, 2723, 710208] C703 29) [137, 5446, 4573897] C703
149) [5556521, 3123, 1049152] C703 24) [97, 6246, 5556521] C703
150) [7330457, 2715, 10192] C703 9) [13, 5430, 7330457] C703
151) [8466361, 3019, 162000] C703 5) [5, 6038, 8466361] C703
152) [8564681, 3235, 475136] C703 15) [29, 6470, 8564681] C703
153) [9370033, 3335, 438048] C703 7) [8, 6670, 9370033] C703
154) [10183193, 3195, 6208] C703 25) [97, 6390, 10183193] C703
155) [10319233, 3391, 294912] C703 8) [8, 6782, 10319233] C703
156) [10743017, 3283, 8768] C703 30) [137, 6566, 10743017] C703
157) [14345761, 3791, 6480] C703 2) [5, 7582, 14345761] C703
158) [15717641, 3971, 12800] C703 6) [8, 7942, 15717641] C703
159) [16887961, 4123, 27792] C703 32) [193, 8246, 16887961] C703
160) [21416089, 4763, 317520] C703 4) [5, 9526, 21416089] C703
161) [21639889, 4663, 25920] C703 1) [5, 9326, 21639889] C703