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 C707 non-normal (D4) quartic CM field invariants: 215 fields

K Quartic invariants Cl(OK) Igusa invariants Kr Reflex invariants Cl(OKr) Igusa invariants
1) [5, 10726, 26961769] C707 213) [26961769, 5363, 450000] C707
2) [5, 6158, 9454321] C707 201) [9454321, 3079, 6480] C707
3) [5, 9974, 22278169] C707 211) [22278169, 4987, 648000] C707
4) [5, 7881, 12808009] C707 207) [12808009, 4067, 933120] C707
5) [5, 10534, 27709289] C707 ---) [27709289, 5267, 8000] C2121
6) [5, 6398, 8881601] C707 ---) [8881601, 3199, 338000] C2121
7) [5, 6878, 11823841] C707 ---) [11823841, 3439, 720] C2121
8) [5, 8558, 18304721] C707 ---) [18304721, 4279, 1280] C3535
9) [5, 9902, 24120401] C707 ---) [24120401, 4951, 98000] C2121
10) [5, 11926, 35165369] C707 215) [35165369, 5963, 98000] C707
11) [5, 7262, 12351841] C707 205) [12351841, 3631, 208080] C707
12) [8, 4874, 4103441] C707 188) [4103441, 2437, 458882] C707
13) [8, 3934, 3609889] C707 ---) [3609889, 1967, 64800] C2121
14) [8, 4798, 4695233] C707 189) [4695233, 2399, 264992] C707
15) [8, 5998, 8453201] C707 199) [8453201, 2999, 135200] C707
16) [8, 7822, 9323953] C707 200) [9323953, 3911, 1492992] C707
17) [8, 8062, 10053761] C707 203) [10053761, 4031, 1548800] C707
18) [8, 6718, 11098049] C707 204) [11098049, 3359, 46208] C707
19) [8, 5470, 7314337] C707 195) [7314337, 2735, 41472] C707
20) [8, 5482, 3911153] C707 187) [3911153, 2741, 900482] C707
21) [8, 3918, 3786481] C707 185) [3786481, 1959, 12800] C707
22) [8, 7054, 12402737] C707 206) [12402737, 3527, 9248] C707
23) [8, 4190, 3725473] C707 184) [3725473, 2095, 165888] C707
24) [8, 5402, 4190369] C707 ---) [4190369, 2701, 776258] C6363
25) [8, 4910, 5363473] C707 192) [5363473, 2455, 165888] C707
26) [8, 4126, 3882721] C707 186) [3882721, 2063, 93312] C707
27) [13, 7334, 13327081] C707 208) [13327081, 3667, 29952] C707
28) [13, 9998, 24870193] C707 212) [24870193, 4999, 29952] C707
29) [29, 2422, 1428937] C707 180) [1428937, 1211, 9396] C707
30) [29, 4454, 4929833] C707 190) [4929833, 2227, 7424] C707
31) [29, 3414, 2884153] C707 183) [2884153, 1707, 7424] C707
32) [41, 10166, 25826393] C707 ---) [25826393, 5083, 2624] C2121
33) [41, 10246, 26234633] C707 ---) [26234633, 5123, 2624] C28987
34) [61, 4862, 5593537] C707 193) [5593537, 2431, 79056] C707
35) [61, 3078, 1369097] C707 179) [1369097, 1539, 249856] C707
36) [61, 1918, 603457] C707 ---) [603457, 959, 79056] C2121
37) [73, 2334, 165857] C707 154) [165857, 1167, 299008] C707
38) [73, 2178, 1101533] C707 ---) [1101533, 1089, 21097] C2121
39) [89, 7478, 13615577] C707 209) [13615577, 3739, 91136] C707
40) [89, 6806, 8299513] C707 197) [8299513, 3403, 820224] C707
41) [89, 2762, 1889717] C707 182) [1889717, 1381, 4361] C707
42) [89, 11846, 34939529] C707 214) [34939529, 5923, 35600] C707
43) [97, 5910, 8427833] C707 198) [8427833, 2955, 76048] C707
44) [97, 5670, 7639913] C707 196) [7639913, 2835, 99328] C707
45) [97, 1818, 816581] C707 174) [816581, 909, 2425] C707
46) [109, 3054, 545873] C707 168) [545873, 1527, 446464] C707
47) [109, 1926, 920393] C707 ---) [920393, 963, 1744] C2121
48) [109, 5870, 6354001] C707 194) [6354001, 2935, 565056] C707
49) [113, 6806, 9490361] C707 202) [9490361, 3403, 522512] C707
50) [113, 766, 139457] C707 152) [139457, 383, 1808] C707
51) [137, 1243, 353348] C707 ---) [88337, 2486, 131657] C2121
52) [137, 4646, 4966697] C707 191) [4966697, 2323, 107408] C707
53) [137, 7526, 13730537] C707 210) [13730537, 3763, 107408] C707
54) [157, 2262, 1118393] C707 ---) [1118393, 1131, 40192] C2121
55) [173, 1750, 721337] C707 172) [721337, 875, 11072] C707
56) [173, 1630, 653153] C707 170) [653153, 815, 2768] C707
57) [181, 2070, 885881] C707 ---) [885881, 1035, 46336] C3535
58) [193, 406, 13417] C707 126) [13417, 203, 6948] C707
59) [197, 2294, 1265177] C707 178) [1265177, 1147, 12608] C707
60) [233, 3022, 2223473] C707 147) [45377, 1511, 14912] C707
61) [397, 1938, 937373] C707 175) [937373, 969, 397] C707
62) [421, 789, 150473] C707 153) [150473, 1578, 20629] C707
63) [433, 510, 37313] C707 145) [37313, 255, 6928] C707
64) [461, 1286, 295433] C707 161) [295433, 643, 29504] C707
65) [509, 886, 122953] C707 ---) [122953, 443, 18324] C2121
66) [509, 1342, 319937] C707 162) [319937, 671, 32576] C707
67) [557, 5150, 606113] C707 169) [606113, 2575, 1506128] C707
68) [569, 2534, 1568873] C707 181) [1568873, 1267, 9104] C707
69) [577, 1458, 529133] C707 ---) [4373, 729, 577] C101
70) [593, 1066, 281717] C707 159) [281717, 533, 593] C707
71) [613, 1782, 166169] C707 155) [166169, 891, 156928] C707
72) [673, 1602, 186653] C707 156) [186653, 801, 113737] C707
73) [677, 1222, 329993] C707 163) [329993, 611, 10832] C707
74) [701, 2414, 335249] C707 164) [335249, 1207, 280400] C707
75) [757, 633, 95441] C707 151) [95441, 1266, 18925] C707
76) [769, 2631, 761408] C707 123) [11897, 1811, 150724] C707
77) [773, 646, 91961] C707 150) [91961, 323, 3092] C707
78) [929, 2134, 1079033] C707 177) [1079033, 1067, 14864] C707
79) [941, 1073, 287597] C707 160) [287597, 2146, 941] C707
80) [1021, 513, 65537] C707 ---) [65537, 1026, 1021] C7 x C2121
81) [1021, 1341, 443189] C707 ---) [443189, 2682, 25525] C2121
82) [1021, 3109, 2230393] C707 ---) [18433, 3479, 588096] C3535
83) [1117, 969, 234461] C707 157) [234461, 1938, 1117] C707
84) [1181, 1058, 161741] C707 ---) [161741, 529, 29525] C2121
85) [1553, 682, 60373] C707 148) [60373, 341, 13977] C707
86) [1637, 1306, 262709] C707 158) [262709, 653, 40925] C707
87) [1741, 1706, 664933] C707 171) [664933, 853, 15669] C707
88) [1877, 1730, 380333] C707 165) [380333, 865, 91973] C707
89) [2017, 2183, 1150528] C707 136) [17977, 4366, 163377] C707
90) [2161, 1163, 272772] C707 120) [7577, 2326, 261481] C707
91) [2333, 934, 68777] C707 149) [68777, 467, 37328] C707
92) [2549, 4078, 2689297] C707 131) [15913, 2039, 367056] C707
93) [2549, 3893, 3094897] C707 138) [18313, 7467, 2946644] C707
94) [2729, 5542, 299225] C707 124) [11969, 2771, 1844804] C707
95) [2953, 4018, 3079309] C707 ---) [5821, 2009, 239193] C2121
96) [3049, 4738, 233725] C707 122) [9349, 2369, 1344609] C707
97) [3109, 5129, 6557229] C707 129) [14869, 6829, 10822429] C707
98) [3169, 819, 71828] C707 ---) [17957, 1638, 383449] C7 x C707
99) [3209, 2943, 1875700] C707 140) [18757, 5886, 1158449] C707
100) [3301, 3001, 105025] C707 104) [4201, 2671, 1320400] C707
101) [3541, 4421, 168813] C707 139) [18757, 7529, 14054229] C707
102) [3617, 482, 43613] C707 146) [43613, 241, 3617] C707
103) [3697, 6131, 6993316] C707 128) [14449, 4507, 133092] C707
104) [4201, 2671, 1320400] C707 100) [3301, 3001, 105025] C707
105) [4241, 1871, 874100] C707 121) [8741, 3742, 4241] C707
106) [4673, 3018, 15349] C707 ---) [15349, 1509, 565433] C2121
107) [4721, 838, 100025] C707 ---) [4001, 419, 18884] C2121
108) [4789, 2245, 109449] C707 ---) [12161, 4490, 4602229] C7777
109) [4793, 6871, 58612] C707 ---) [14653, 8445, 1385177] C2121
110) [4813, 9409, 17356621] C707 137) [18061, 7349, 7320573] C707
111) [5189, 10181, 21698425] C707 134) [17713, 5219, 747216] C707
112) [5437, 7569, 2055209] C707 ---) [12161, 4371, 4262608] C7777
113) [5441, 5207, 1031156] C707 ---) [5261, 3013, 658361] C2121
114) [5449, 3346, 161613] C707 ---) [17957, 1673, 659329] C7 x C707
115) [5557, 2273, 123273] C707 127) [13697, 4546, 4673437] C707
116) [5573, 646, 15161] C707 130) [15161, 323, 22292] C707
117) [5653, 2461, 155997] C707 133) [17333, 4922, 5432533] C707
118) [5717, 6609, 10678177] C707 125) [12697, 5875, 3292992] C707
119) [5801, 4994, 6026173] C707 132) [16693, 2497, 52209] C707
120) [7577, 2326, 261481] C707 90) [2161, 1163, 272772] C707
121) [8741, 3742, 4241] C707 105) [4241, 1871, 874100] C707
122) [9349, 2369, 1344609] C707 96) [3049, 4738, 233725] C707
123) [11897, 1811, 150724] C707 76) [769, 2631, 761408] C707
124) [11969, 2771, 1844804] C707 94) [2729, 5542, 299225] C707
125) [12697, 5875, 3292992] C707 118) [5717, 6609, 10678177] C707
126) [13417, 203, 6948] C707 58) [193, 406, 13417] C707
127) [13697, 4546, 4673437] C707 115) [5557, 2273, 123273] C707
128) [14449, 4507, 133092] C707 103) [3697, 6131, 6993316] C707
129) [14869, 6829, 10822429] C707 97) [3109, 5129, 6557229] C707
130) [15161, 323, 22292] C707 116) [5573, 646, 15161] C707
131) [15913, 2039, 367056] C707 92) [2549, 4078, 2689297] C707
132) [16693, 2497, 52209] C707 119) [5801, 4994, 6026173] C707
133) [17333, 4922, 5432533] C707 117) [5653, 2461, 155997] C707
134) [17713, 5219, 747216] C707 111) [5189, 10181, 21698425] C707
135) [17957, 2485, 246413] C707 ---) [293, 1345, 17957] C101
136) [17977, 4366, 163377] C707 89) [2017, 2183, 1150528] C707
137) [18061, 7349, 7320573] C707 110) [4813, 9409, 17356621] C707
138) [18313, 7467, 2946644] C707 93) [2549, 3893, 3094897] C707
139) [18757, 7529, 14054229] C707 101) [3541, 4421, 168813] C707
140) [18757, 5886, 1158449] C707 99) [3209, 2943, 1875700] C707
141) [26317, 737, 129213] C707 ---) [293, 1474, 26317] C101
142) [26713, 831, 5684] C707 ---) [29, 729, 26713] C101
143) [30817, 1630, 171153] C707 ---) [2113, 815, 123268] C101
144) [33941, 641, 26353] C707 ---) [73, 1282, 305469] C101
145) [37313, 255, 6928] C707 63) [433, 510, 37313] C707
146) [43613, 241, 3617] C707 102) [3617, 482, 43613] C707
147) [45377, 1511, 14912] C707 60) [233, 3022, 2223473] C707
148) [60373, 341, 13977] C707 85) [1553, 682, 60373] C707
149) [68777, 467, 37328] C707 91) [2333, 934, 68777] C707
150) [91961, 323, 3092] C707 77) [773, 646, 91961] C707
151) [95441, 1266, 18925] C707 75) [757, 633, 95441] C707
152) [139457, 383, 1808] C707 50) [113, 766, 139457] C707
153) [150473, 1578, 20629] C707 62) [421, 789, 150473] C707
154) [165857, 1167, 299008] C707 37) [73, 2334, 165857] C707
155) [166169, 891, 156928] C707 71) [613, 1782, 166169] C707
156) [186653, 801, 113737] C707 72) [673, 1602, 186653] C707
157) [234461, 1938, 1117] C707 83) [1117, 969, 234461] C707
158) [262709, 653, 40925] C707 86) [1637, 1306, 262709] C707
159) [281717, 533, 593] C707 70) [593, 1066, 281717] C707
160) [287597, 2146, 941] C707 79) [941, 1073, 287597] C707
161) [295433, 643, 29504] C707 64) [461, 1286, 295433] C707
162) [319937, 671, 32576] C707 66) [509, 1342, 319937] C707
163) [329993, 611, 10832] C707 73) [677, 1222, 329993] C707
164) [335249, 1207, 280400] C707 74) [701, 2414, 335249] C707
165) [380333, 865, 91973] C707 88) [1877, 1730, 380333] C707
166) [470209, 727, 14580] C707 ---) [5, 1454, 470209] C101
167) [521369, 787, 24500] C707 ---) [5, 1574, 521369] C101
168) [545873, 1527, 446464] C707 46) [109, 3054, 545873] C707
169) [606113, 2575, 1506128] C707 67) [557, 5150, 606113] C707
170) [653153, 815, 2768] C707 56) [173, 1630, 653153] C707
171) [664933, 853, 15669] C707 87) [1741, 1706, 664933] C707
172) [721337, 875, 11072] C707 55) [173, 1750, 721337] C707
173) [801001, 899, 1800] C707 ---) [8, 1798, 801001] C101
174) [816581, 909, 2425] C707 45) [97, 1818, 816581] C707
175) [937373, 969, 397] C707 61) [397, 1938, 937373] C707
176) [1033061, 1541, 335405] C707 ---) [5, 2033, 1033061] C101
177) [1079033, 1067, 14864] C707 78) [929, 2134, 1079033] C707
178) [1265177, 1147, 12608] C707 59) [197, 2294, 1265177] C707
179) [1369097, 1539, 249856] C707 35) [61, 3078, 1369097] C707
180) [1428937, 1211, 9396] C707 29) [29, 2422, 1428937] C707
181) [1568873, 1267, 9104] C707 68) [569, 2534, 1568873] C707
182) [1889717, 1381, 4361] C707 41) [89, 2762, 1889717] C707
183) [2884153, 1707, 7424] C707 31) [29, 3414, 2884153] C707
184) [3725473, 2095, 165888] C707 23) [8, 4190, 3725473] C707
185) [3786481, 1959, 12800] C707 21) [8, 3918, 3786481] C707
186) [3882721, 2063, 93312] C707 26) [8, 4126, 3882721] C707
187) [3911153, 2741, 900482] C707 20) [8, 5482, 3911153] C707
188) [4103441, 2437, 458882] C707 12) [8, 4874, 4103441] C707
189) [4695233, 2399, 264992] C707 14) [8, 4798, 4695233] C707
190) [4929833, 2227, 7424] C707 30) [29, 4454, 4929833] C707
191) [4966697, 2323, 107408] C707 52) [137, 4646, 4966697] C707
192) [5363473, 2455, 165888] C707 25) [8, 4910, 5363473] C707
193) [5593537, 2431, 79056] C707 34) [61, 4862, 5593537] C707
194) [6354001, 2935, 565056] C707 48) [109, 5870, 6354001] C707
195) [7314337, 2735, 41472] C707 19) [8, 5470, 7314337] C707
196) [7639913, 2835, 99328] C707 44) [97, 5670, 7639913] C707
197) [8299513, 3403, 820224] C707 40) [89, 6806, 8299513] C707
198) [8427833, 2955, 76048] C707 43) [97, 5910, 8427833] C707
199) [8453201, 2999, 135200] C707 15) [8, 5998, 8453201] C707
200) [9323953, 3911, 1492992] C707 16) [8, 7822, 9323953] C707
201) [9454321, 3079, 6480] C707 2) [5, 6158, 9454321] C707
202) [9490361, 3403, 522512] C707 49) [113, 6806, 9490361] C707
203) [10053761, 4031, 1548800] C707 17) [8, 8062, 10053761] C707
204) [11098049, 3359, 46208] C707 18) [8, 6718, 11098049] C707
205) [12351841, 3631, 208080] C707 11) [5, 7262, 12351841] C707
206) [12402737, 3527, 9248] C707 22) [8, 7054, 12402737] C707
207) [12808009, 4067, 933120] C707 4) [5, 7881, 12808009] C707
208) [13327081, 3667, 29952] C707 27) [13, 7334, 13327081] C707
209) [13615577, 3739, 91136] C707 39) [89, 7478, 13615577] C707
210) [13730537, 3763, 107408] C707 53) [137, 7526, 13730537] C707
211) [22278169, 4987, 648000] C707 3) [5, 9974, 22278169] C707
212) [24870193, 4999, 29952] C707 28) [13, 9998, 24870193] C707
213) [26961769, 5363, 450000] C707 1) [5, 10726, 26961769] C707
214) [34939529, 5923, 35600] C707 42) [89, 11846, 34939529] C707
215) [35165369, 5963, 98000] C707 10) [5, 11926, 35165369] C707