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 C915 non-normal (D4) quartic CM field invariants: 189 fields

K Quartic invariants Cl(OK) Igusa invariants Kr Reflex invariants Cl(OKr) Igusa invariants
1) [8, 4894, 5946337] C915 186) [5946337, 2447, 10368] C915
2) [13, 10173, 25821701] C915 ---) [25821701, 18209, 24793093] C6405
3) [17, 2606, 1628177] C915 ---) [1628177, 1303, 17408] C3 x C28365
4) [61, 3462, 1996937] C915 180) [1996937, 1731, 249856] C915
5) [97, 1854, 238529] C915 146) [238529, 927, 155200] C915
6) [101, 4390, 4714601] C915 185) [4714601, 2195, 25856] C915
7) [149, 2582, 1199417] C915 174) [1199417, 1291, 116816] C915
8) [173, 3118, 2386193] C915 181) [2386193, 1559, 11072] C915
9) [173, 3254, 1307417] C915 175) [1307417, 1627, 334928] C915
10) [241, 2094, 109073] C915 139) [109073, 1047, 246784] C915
11) [241, 1098, 277301] C915 148) [277301, 549, 6025] C915
12) [293, 2102, 1029593] C915 171) [1029593, 1051, 18752] C915
13) [349, 1206, 341273] C915 153) [341273, 603, 5584] C915
14) [373, 1686, 615161] C915 164) [615161, 843, 23872] C915
15) [389, 1598, 538817] C915 159) [538817, 799, 24896] C915
16) [401, 1023, 198976] C915 ---) [3109, 625, 3609] C183
17) [401, 583, 76852] C915 ---) [19213, 1166, 32481] C3 x C183
18) [461, 1598, 608897] C915 163) [608897, 799, 7376] C915
19) [461, 2038, 300761] C915 151) [300761, 1019, 184400] C915
20) [509, 2726, 1043369] C915 172) [1043369, 1363, 203600] C915
21) [521, 523, 39076] C915 93) [9769, 1046, 117225] C915
22) [521, 1195, 69284] C915 119) [17321, 2390, 1150889] C915
23) [541, 1150, 19009] C915 129) [19009, 575, 77904] C915
24) [613, 1545, 578213] C915 162) [578213, 3090, 74173] C915
25) [641, 918, 200425] C915 ---) [8017, 459, 2564] C3 x C915
26) [677, 1581, 616597] C915 166) [616597, 3162, 33173] C915
27) [769, 342, 16937] C915 118) [16937, 171, 3076] C915
28) [797, 1249, 373861] C915 155) [373861, 2498, 64557] C915
29) [1013, 1377, 443389] C915 157) [443389, 2754, 122573] C915
30) [1049, 1138, 285997] C915 150) [285997, 569, 9441] C915
31) [1061, 1149, 189733] C915 ---) [189733, 2298, 561269] C5 x C915
32) [1061, 1329, 396733] C915 156) [396733, 2658, 179309] C915
33) [1093, 258, 12269] C915 ---) [12269, 129, 1093] C3 x C183
34) [1193, 850, 175853] C915 144) [175853, 425, 1193] C915
35) [1193, 4118, 2693353] C915 113) [15937, 2059, 386532] C915
36) [1429, 1145, 267381] C915 ---) [3301, 2141, 630189] C183
37) [1801, 4422, 18617] C915 127) [18617, 2211, 1217476] C915
38) [2113, 1187, 288324] C915 84) [8009, 2374, 255673] C915
39) [2113, 3551, 489492] C915 107) [13597, 4385, 1540377] C915
40) [2153, 462, 18913] C915 ---) [18913, 231, 8612] C183
41) [2213, 1657, 8681] C915 ---) [8681, 3314, 2710925] C305
42) [2377, 1939, 625572] C915 120) [17377, 3878, 1257433] C915
43) [2473, 5042, 6345549] C915 ---) [14389, 2521, 2473] C3 x C915
44) [2557, 1162, 245509] C915 ---) [2029, 581, 23013] C2135
45) [2609, 3327, 1670800] C915 69) [4177, 1867, 845316] C915
46) [2617, 6466, 2821117] C915 117) [16693, 3233, 1907793] C915
47) [2633, 2067, 719908] C915 60) [3673, 3351, 2696192] C915
48) [2789, 3269, 406225] C915 114) [16249, 6538, 9061461] C915
49) [3121, 506, 51525] C915 ---) [229, 253, 3121] C3 x C183
50) [3181, 677, 107425] C915 ---) [4297, 1354, 28629] C183
51) [3221, 1453, 101825] C915 ---) [4073, 2906, 1703909] C305
52) [3253, 3141, 6389] C915 ---) [6389, 3309, 2735773] C183
53) [3253, 581, 18517] C915 ---) [18517, 1162, 263493] C183
54) [3329, 5270, 498281] C915 94) [10169, 2635, 1611236] C915
55) [3329, 5931, 6456400] C915 ---) [16141, 5489, 749025] C3 x C915
56) [3457, 6051, 7555652] C915 97) [11177, 3207, 221248] C915
57) [3517, 3037, 18913] C915 128) [18913, 6074, 9147717] C915
58) [3517, 253, 8089] C915 86) [8089, 506, 31653] C915
59) [3617, 6563, 7620548] C915 ---) [11273, 4091, 4181252] C5 x C915
60) [3673, 3351, 2696192] C915 47) [2633, 2067, 719908] C915
61) [3769, 330, 12149] C915 100) [12149, 165, 3769] C915
62) [3833, 1994, 978677] C915 130) [19973, 997, 3833] C915
63) [3889, 8043, 981056] C915 ---) [15329, 4171, 1555600] C305
64) [3929, 619, 16228] C915 67) [4057, 1238, 318249] C915
65) [3989, 605, 10729] C915 95) [10729, 1210, 323109] C915
66) [4049, 4862, 5650625] C915 90) [9041, 2431, 64784] C915
67) [4057, 1238, 318249] C915 64) [3929, 619, 16228] C915
68) [4177, 1219, 195012] C915 ---) [5417, 2438, 705913] C6405
69) [4177, 1867, 845316] C915 45) [2609, 3327, 1670800] C915
70) [4241, 5791, 1766900] C915 123) [17669, 7369, 12829025] C915
71) [4261, 5157, 4857977] C915 ---) [13457, 5867, 6152884] C11895
72) [4957, 8749, 8417977] C915 112) [15913, 4519, 3350932] C915
73) [4973, 689, 17977] C915 124) [17977, 1378, 402813] C915
74) [5209, 2975, 1742544] C915 ---) [12101, 5950, 1880449] C5 x C915
75) [5261, 2893, 1512337] C915 ---) [5233, 4759, 1704564] C305
76) [5281, 1466, 9189] C915 ---) [1021, 733, 132025] C305
77) [5569, 9031, 9361728] C915 115) [16253, 5133, 1609441] C915
78) [5801, 8191, 4763600] C915 99) [11909, 7637, 5574761] C915
79) [5857, 4838, 5008153] C915 108) [13873, 2419, 210852] C915
80) [5897, 2755, 292048] C915 ---) [18253, 5510, 6421833] C5 x C915
81) [6637, 137, 3033] C915 ---) [337, 274, 6637] C305
82) [7229, 4901, 1304293] C915 ---) [3613, 2673, 1221701] C183
83) [7817, 983, 5108] C915 ---) [1277, 1966, 945857] C183
84) [8009, 2374, 255673] C915 38) [2113, 1187, 288324] C915
85) [8069, 2934, 86425] C915 ---) [3457, 1467, 516416] C305
86) [8089, 506, 31653] C915 58) [3517, 253, 8089] C915
87) [8597, 2881, 2021309] C915 ---) [3821, 5701, 214925] C305
88) [8597, 4449, 2006077] C915 ---) [5557, 7421, 696357] C305
89) [8837, 2261, 780949] C915 ---) [4621, 4522, 1988325] C305
90) [9041, 2431, 64784] C915 66) [4049, 4862, 5650625] C915
91) [9133, 1914, 2549] C915 ---) [2549, 957, 228325] C305
92) [9281, 3159, 2492500] C915 ---) [997, 1961, 751761] C305
93) [9769, 1046, 117225] C915 21) [521, 523, 39076] C915
94) [10169, 2635, 1611236] C915 54) [3329, 5270, 498281] C915
95) [10729, 1210, 323109] C915 65) [3989, 605, 10729] C915
96) [10949, 3041, 2243489] C915 ---) [4241, 6082, 273725] C305
97) [11177, 3207, 221248] C915 56) [3457, 6051, 7555652] C915
98) [11789, 3101, 1340093] C915 ---) [4637, 6202, 4255829] C305
99) [11909, 7637, 5574761] C915 78) [5801, 8191, 4763600] C915
100) [12149, 165, 3769] C915 61) [3769, 330, 12149] C915
101) [12401, 3466, 572693] C915 ---) [4733, 1733, 607649] C305
102) [12401, 3967, 558100] C915 ---) [5581, 7934, 13504689] C305
103) [12401, 3131, 1331600] C915 ---) [3329, 6262, 4476761] C305
104) [13229, 1050, 222709] C915 ---) [421, 525, 13229] C183
105) [13229, 3129, 698125] C915 ---) [1117, 2729, 119061] C183
106) [13537, 5243, 19156] C915 ---) [4789, 6413, 8460625] C305
107) [13597, 4385, 1540377] C915 39) [2113, 3551, 489492] C915
108) [13873, 2419, 210852] C915 79) [5857, 4838, 5008153] C915
109) [13877, 3230, 609937] C915 ---) [1153, 1615, 499572] C305
110) [15061, 949, 40653] C915 ---) [4517, 1898, 737989] C305
111) [15121, 990, 3089] C915 ---) [3089, 495, 60484] C183
112) [15913, 4519, 3350932] C915 72) [4957, 8749, 8417977] C915
113) [15937, 2059, 386532] C915 35) [1193, 4118, 2693353] C915
114) [16249, 6538, 9061461] C915 48) [2789, 3269, 406225] C915
115) [16253, 5133, 1609441] C915 77) [5569, 9031, 9361728] C915
116) [16477, 1709, 231741] C915 ---) [2861, 3418, 1993717] C305
117) [16693, 3233, 1907793] C915 46) [2617, 6466, 2821117] C915
118) [16937, 171, 3076] C915 27) [769, 342, 16937] C915
119) [17321, 2390, 1150889] C915 22) [521, 1195, 69284] C915
120) [17377, 3878, 1257433] C915 42) [2377, 1939, 625572] C915
121) [17417, 5627, 7563088] C915 ---) [2797, 4581, 2107457] C305
122) [17477, 3986, 546557] C915 ---) [4517, 1993, 856373] C305
123) [17669, 7369, 12829025] C915 70) [4241, 5791, 1766900] C915
124) [17977, 1378, 402813] C915 73) [4973, 689, 17977] C915
125) [18253, 201, 5537] C915 ---) [113, 402, 18253] C183
126) [18329, 1471, 426404] C915 ---) [881, 2942, 458225] C61
127) [18617, 2211, 1217476] C915 37) [1801, 4422, 18617] C915
128) [18913, 6074, 9147717] C915 57) [3517, 3037, 18913] C915
129) [19009, 575, 77904] C915 23) [541, 1150, 19009] C915
130) [19973, 997, 3833] C915 62) [3833, 1994, 978677] C915
131) [24281, 659, 102500] C915 ---) [41, 955, 97124] C305
132) [36389, 1801, 729025] C915 ---) [241, 2955, 582224] C305
133) [43889, 1051, 1844] C915 ---) [461, 2102, 1097225] C183
134) [45989, 1050, 91669] C915 ---) [109, 525, 45989] C183
135) [56101, 317, 11097] C915 ---) [137, 634, 56101] C183
136) [75653, 1226, 73157] C915 ---) [1493, 613, 75653] C305
137) [79133, 537, 52309] C915 ---) [181, 1074, 79133] C183
138) [92401, 931, 8788] C915 ---) [13, 649, 92401] C183
139) [109073, 1047, 246784] C915 10) [241, 2094, 109073] C915
140) [111341, 337, 557] C915 ---) [557, 674, 111341] C305
141) [143833, 3102, 104273] C915 ---) [617, 1551, 575332] C305
142) [155201, 607, 53312] C915 ---) [17, 1214, 155201] C305
143) [169097, 1847, 472384] C915 ---) [61, 2937, 169097] C305
144) [175853, 425, 1193] C915 34) [1193, 850, 175853] C915
145) [216217, 467, 468] C915 ---) [13, 934, 216217] C305
146) [238529, 927, 155200] C915 5) [97, 1854, 238529] C915
147) [254993, 2459, 937936] C915 ---) [61, 3261, 254993] C305
148) [277301, 549, 6025] C915 11) [241, 1098, 277301] C915
149) [279317, 661, 39401] C915 ---) [41, 1322, 279317] C183
150) [285997, 569, 9441] C915 30) [1049, 1138, 285997] C915
151) [300761, 1019, 184400] C915 19) [461, 2038, 300761] C915
152) [312281, 635, 22736] C915 ---) [29, 1270, 312281] C183
153) [341273, 603, 5584] C915 13) [349, 1206, 341273] C915
154) [341321, 739, 51200] C915 ---) [8, 1478, 341321] C61
155) [373861, 2498, 64557] C915 28) [797, 1249, 373861] C915
156) [396733, 2658, 179309] C915 32) [1061, 1329, 396733] C915
157) [443389, 2754, 122573] C915 29) [1013, 1377, 443389] C915
158) [494069, 2874, 88693] C915 ---) [733, 1437, 494069] C3 x C915
159) [538817, 799, 24896] C915 15) [389, 1598, 538817] C915
160) [560353, 911, 67392] C915 ---) [13, 1822, 560353] C305
161) [572969, 3839, 103424] C915 ---) [101, 7573, 14324225] C305
162) [578213, 3090, 74173] C915 24) [613, 1545, 578213] C915
163) [608897, 799, 7376] C915 18) [461, 1598, 608897] C915
164) [615161, 843, 23872] C915 14) [373, 1686, 615161] C915
165) [616157, 785, 17] C915 ---) [17, 1570, 616157] C183
166) [616597, 3162, 33173] C915 26) [677, 1581, 616597] C915
167) [677953, 863, 16704] C915 ---) [29, 1726, 677953] C305
168) [689321, 979, 67280] C915 ---) [5, 1777, 689321] C183
169) [802721, 943, 21632] C915 ---) [8, 1886, 802721] C305
170) [881233, 2843, 37888] C915 ---) [37, 5686, 7931097] C183
171) [1029593, 1051, 18752] C915 12) [293, 2102, 1029593] C915
172) [1043369, 1363, 203600] C915 20) [509, 2726, 1043369] C915
173) [1063273, 1091, 31752] C915 ---) [8, 2182, 1063273] C183
174) [1199417, 1291, 116816] C915 7) [149, 2582, 1199417] C915
175) [1307417, 1627, 334928] C915 9) [173, 3254, 1307417] C915
176) [1334797, 1201, 26901] C915 ---) [61, 2402, 1334797] C305
177) [1570193, 1495, 166208] C915 ---) [53, 2990, 1570193] C305
178) [1837393, 1399, 29952] C915 ---) [13, 2798, 1837393] C183
179) [1885729, 2927, 1670400] C915 ---) [29, 5854, 1885729] C305
180) [1996937, 1731, 249856] C915 4) [61, 3462, 1996937] C915
181) [2386193, 1559, 11072] C915 8) [173, 3118, 2386193] C915
182) [2810501, 2501, 861125] C915 ---) [5, 3353, 2810501] C183
183) [2846621, 2329, 644405] C915 ---) [5, 3397, 2846621] C183
184) [3265369, 2011, 194688] C915 ---) [8, 4022, 3265369] C305
185) [4714601, 2195, 25856] C915 6) [101, 4390, 4714601] C915
186) [5946337, 2447, 10368] C915 1) [8, 4894, 5946337] C915
187) [7740377, 3163, 566048] C915 ---) [8, 6326, 7740377] C305
188) [9641881, 3259, 244800] C915 ---) [17, 6518, 9641881] C305
189) [11427209, 4003, 1149200] C915 ---) [17, 8006, 11427209] C305