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 C755 non-normal (D4) quartic CM field invariants: 189 fields

K Quartic invariants Cl(OK) Igusa invariants Kr Reflex invariants Cl(OKr) Igusa invariants
1) [5, 5518, 6964081] C755 180) [6964081, 2759, 162000] C755
2) [5, 11006, 30032129] C755 188) [30032129, 5503, 62720] C755
3) [5, 11534, 32930609] C755 ---) [32930609, 5767, 81920] C2265
4) [5, 10534, 27326569] C755 186) [27326569, 5267, 103680] C755
5) [5, 10846, 27840929] C755 ---) [27840929, 5423, 392000] C17365
6) [5, 9278, 17361601] C755 ---) [17361601, 4639, 1039680] C5285
7) [8, 5054, 6344257] C755 178) [6344257, 2527, 10368] C755
8) [8, 12758, 40640441] C755 ---) [40640441, 6379, 12800] C5 x C755
9) [8, 6542, 10666673] C755 184) [10666673, 3271, 8192] C755
10) [8, 5086, 5287201] C755 175) [5287201, 2543, 294912] C755
11) [8, 5902, 5828401] C755 177) [5828401, 2951, 720000] C755
12) [8, 11366, 31989161] C755 189) [31989161, 5683, 76832] C755
13) [8, 6094, 7873009] C755 182) [7873009, 3047, 352800] C755
14) [8, 6718, 8006081] C755 183) [8006081, 3359, 819200] C755
15) [8, 6814, 7460449] C755 181) [7460449, 3407, 1036800] C755
16) [8, 3982, 3656753] C755 172) [3656753, 1991, 76832] C755
17) [13, 4734, 5519489] C755 176) [5519489, 2367, 20800] C755
18) [17, 2246, 1032377] C755 158) [1032377, 1123, 57188] C755
19) [17, 4222, 1044353] C755 ---) [1044353, 2111, 852992] C5 x C6795
20) [17, 3182, 1795793] C755 ---) [1795793, 1591, 183872] C2265
21) [17, 2734, 1015697] C755 157) [1015697, 1367, 213248] C755
22) [29, 3038, 2121761] C755 168) [2121761, 1519, 46400] C755
23) [37, 2550, 1587737] C755 161) [1587737, 1275, 9472] C755
24) [37, 7142, 11025769] C755 185) [11025769, 3571, 431568] C755
25) [37, 6425, 8438697] C755 156) [937633, 3215, 2349648] C755
26) [53, 4870, 3269897] C755 171) [3269897, 2435, 664832] C755
27) [53, 4126, 1596641] C755 163) [1596641, 2063, 664832] C755
28) [61, 2598, 1215017] C755 ---) [1215017, 1299, 118096] C2265
29) [61, 1534, 553153] C755 152) [553153, 767, 8784] C755
30) [73, 2394, 1250309] C755 159) [1250309, 1197, 45625] C755
31) [89, 5398, 6464377] C755 179) [6464377, 2699, 205056] C755
32) [89, 10918, 29436137] C755 187) [29436137, 5459, 91136] C755
33) [89, 1630, 299681] C755 149) [299681, 815, 91136] C755
34) [113, 1802, 757109] C755 ---) [757109, 901, 13673] C2265
35) [113, 3470, 399473] C755 150) [399473, 1735, 652688] C755
36) [157, 4550, 3728713] C755 173) [3728713, 2275, 361728] C755
37) [181, 6702, 10487825] C755 151) [419513, 3351, 185344] C755
38) [193, 1383, 448016] C755 138) [28001, 2087, 521872] C755
39) [197, 2974, 1404257] C755 ---) [1404257, 1487, 201728] C2265
40) [197, 1761, 766957] C755 155) [766957, 3522, 33293] C755
41) [233, 1227, 130276] C755 ---) [32569, 2454, 984425] C2265
42) [277, 1045, 167677] C755 146) [167677, 2090, 421317] C755
43) [293, 2570, 1593797] C755 162) [1593797, 1285, 14357] C755
44) [337, 9238, 19178361] C755 169) [2130929, 4619, 539200] C755
45) [401, 839, 147008] C755 ---) [2297, 551, 6416] C151
46) [401, 403, 38096] C755 ---) [2381, 806, 10025] C151
47) [433, 1091, 206532] C755 105) [5737, 1351, 443392] C755
48) [541, 7414, 10279449] C755 ---) [1142161, 3707, 865600] C2265
49) [557, 1802, 756101] C755 ---) [756101, 901, 13925] C5 x C755
50) [557, 1581, 601357] C755 154) [601357, 3162, 94133] C755
51) [617, 6838, 1580633] C755 ---) [1580633, 3419, 2527232] C2265
52) [653, 7414, 13700057] C755 ---) [279593, 3707, 10448] C2265
53) [661, 702, 80897] C755 143) [80897, 351, 10576] C755
54) [757, 6894, 6019601] C755 ---) [122849, 3447, 1465552] C5 x C755
55) [857, 3670, 1392697] C755 160) [1392697, 1835, 493632] C755
56) [937, 1523, 433476] C755 ---) [12041, 3046, 585625] C5 x C755
57) [1033, 3607, 2093328] C755 128) [14537, 3075, 2185828] C755
58) [1093, 1414, 62649] C755 ---) [6961, 707, 109300] C151
59) [1109, 758, 125897] C755 ---) [125897, 379, 4436] C5 x C2265
60) [1109, 2626, 1613069] C755 164) [1613069, 1313, 27725] C755
61) [1109, 737, 128861] C755 145) [128861, 1474, 27725] C755
62) [1277, 397, 36529] C755 140) [36529, 794, 11493] C755
63) [1429, 1794, 798893] C755 ---) [2213, 897, 1429] C453
64) [1429, 1389, 139013] C755 ---) [2837, 1489, 241501] C151
65) [1613, 957, 83389] C755 ---) [83389, 1914, 582293] C5 x C755
66) [1777, 1638, 557033] C755 153) [557033, 819, 28432] C755
67) [2137, 3027, 33476] C755 113) [8369, 3071, 2188288] C755
68) [2153, 1306, 4421] C755 ---) [4421, 653, 105497] C151
69) [2281, 1058, 51741] C755 106) [5749, 529, 57025] C755
70) [2341, 5609, 125289] C755 127) [13921, 4855, 599296] C755
71) [2521, 1154, 242173] C755 ---) [242173, 577, 22689] C2265
72) [2609, 554, 66293] C755 ---) [66293, 277, 2609] C2265
73) [2897, 1582, 208513] C755 147) [208513, 791, 104292] C755
74) [3049, 5875, 7896384] C755 124) [13709, 6129, 9223225] C755
75) [3061, 3606, 2467193] C755 116) [8537, 1803, 195904] C755
76) [3253, 2713, 336393] C755 ---) [4153, 2863, 1873728] C151
77) [3253, 1317, 3413] C755 ---) [3413, 2634, 1720837] C151
78) [3253, 1877, 697801] C755 ---) [4129, 3754, 731925] C151
79) [3373, 1373, 166869] C755 ---) [18541, 2746, 1217653] C2265
80) [3457, 3323, 2033748] C755 110) [6277, 3425, 31113] C755
81) [3529, 1907, 837700] C755 114) [8377, 3814, 285849] C755
82) [3529, 2947, 829300] C755 112) [8293, 5657, 285849] C755
83) [3541, 1565, 144009] C755 ---) [16001, 3130, 1873189] C5 x C755
84) [3617, 955, 75188] C755 135) [18797, 1910, 611273] C755
85) [3769, 635, 24484] C755 109) [6121, 1270, 305289] C755
86) [3853, 2498, 1544589] C755 136) [19069, 1249, 3853] C755
87) [3853, 513, 18593] C755 133) [18593, 1026, 188797] C755
88) [3917, 277, 10369] C755 119) [10369, 554, 35253] C755
89) [4289, 2691, 908608] C755 ---) [14197, 5382, 3607049] C2265
90) [4297, 4919, 5919156] C755 ---) [18269, 8429, 5882593] C2265
91) [4297, 4707, 1000256] C755 ---) [15629, 7773, 4129417] C6795
92) [4297, 755, 55492] C755 126) [13873, 1510, 348057] C755
93) [4349, 8653, 2269597] C755 134) [18757, 5409, 1569989] C755
94) [4397, 7713, 9014689] C755 129) [17041, 6431, 10130688] C755
95) [4549, 2845, 930609] C755 122) [11489, 5690, 4371589] C755
96) [4789, 7778, 4990797] C755 120) [11317, 3889, 2533381] C755
97) [4877, 3009, 1501489] C755 ---) [12409, 6018, 3048125] C6795
98) [4877, 2737, 18313] C755 131) [18313, 5474, 7417917] C755
99) [4993, 1323, 286544] C755 130) [17909, 2646, 604153] C755
100) [5077, 1733, 79389] C755 117) [8821, 3466, 2685733] C755
101) [5189, 4309, 3955625] C755 111) [6329, 3835, 1017044] C755
102) [5501, 1437, 283825] C755 121) [11353, 2874, 929669] C755
103) [5693, 2205, 18553] C755 132) [18553, 4410, 4787813] C755
104) [5693, 3989, 3350377] C755 123) [11593, 7978, 2510613] C755
105) [5737, 1351, 443392] C755 47) [433, 1091, 206532] C755
106) [5749, 529, 57025] C755 69) [2281, 1058, 51741] C755
107) [5801, 6703, 754496] C755 ---) [11789, 5665, 3068729] C2265
108) [5897, 962, 19069] C755 137) [19069, 481, 53073] C755
109) [6121, 1270, 305289] C755 85) [3769, 635, 24484] C755
110) [6277, 3425, 31113] C755 80) [3457, 3323, 2033748] C755
111) [6329, 3835, 1017044] C755 101) [5189, 4309, 3955625] C755
112) [8293, 5657, 285849] C755 82) [3529, 2947, 829300] C755
113) [8369, 3071, 2188288] C755 67) [2137, 3027, 33476] C755
114) [8377, 3814, 285849] C755 81) [3529, 1907, 837700] C755
115) [8501, 2549, 500093] C755 ---) [4133, 5098, 4497029] C151
116) [8537, 1803, 195904] C755 75) [3061, 3606, 2467193] C755
117) [8821, 3466, 2685733] C755 100) [5077, 1733, 79389] C755
118) [9181, 2690, 9549] C755 ---) [1061, 1345, 449869] C151
119) [10369, 554, 35253] C755 88) [3917, 277, 10369] C755
120) [11317, 3889, 2533381] C755 96) [4789, 7778, 4990797] C755
121) [11353, 2874, 929669] C755 102) [5501, 1437, 283825] C755
122) [11489, 5690, 4371589] C755 95) [4549, 2845, 930609] C755
123) [11593, 7978, 2510613] C755 104) [5693, 3989, 3350377] C755
124) [13709, 6129, 9223225] C755 74) [3049, 5875, 7896384] C755
125) [13841, 1247, 219200] C755 ---) [137, 943, 221456] C151
126) [13873, 1510, 348057] C755 92) [4297, 755, 55492] C755
127) [13921, 4855, 599296] C755 70) [2341, 5609, 125289] C755
128) [14537, 3075, 2185828] C755 57) [1033, 3607, 2093328] C755
129) [17041, 6431, 10130688] C755 94) [4397, 7713, 9014689] C755
130) [17909, 2646, 604153] C755 99) [4993, 1323, 286544] C755
131) [18313, 5474, 7417917] C755 98) [4877, 2737, 18313] C755
132) [18553, 4410, 4787813] C755 103) [5693, 2205, 18553] C755
133) [18593, 1026, 188797] C755 87) [3853, 513, 18593] C755
134) [18757, 5409, 1569989] C755 93) [4349, 8653, 2269597] C755
135) [18797, 1910, 611273] C755 84) [3617, 955, 75188] C755
136) [19069, 1249, 3853] C755 86) [3853, 2498, 1544589] C755
137) [19069, 481, 53073] C755 108) [5897, 962, 19069] C755
138) [28001, 2087, 521872] C755 38) [193, 1383, 448016] C755
139) [29033, 203, 3044] C755 ---) [761, 406, 29033] C2265
140) [36529, 794, 11493] C755 62) [1277, 397, 36529] C755
141) [37253, 197, 389] C755 ---) [389, 394, 37253] C151
142) [40637, 241, 4361] C755 ---) [89, 482, 40637] C151
143) [80897, 351, 10576] C755 53) [661, 702, 80897] C755
144) [94621, 1394, 107325] C755 ---) [53, 697, 94621] C151
145) [128861, 1474, 27725] C755 61) [1109, 737, 128861] C755
146) [167677, 2090, 421317] C755 42) [277, 1045, 167677] C755
147) [208513, 791, 104292] C755 73) [2897, 1582, 208513] C755
148) [214657, 2339, 884752] C755 ---) [457, 4678, 1931913] C151
149) [299681, 815, 91136] C755 33) [89, 1630, 299681] C755
150) [399473, 1735, 652688] C755 35) [113, 3470, 399473] C755
151) [419513, 3351, 185344] C755 37) [181, 6702, 10487825] C755
152) [553153, 767, 8784] C755 29) [61, 1534, 553153] C755
153) [557033, 819, 28432] C755 66) [1777, 1638, 557033] C755
154) [601357, 3162, 94133] C755 50) [557, 1581, 601357] C755
155) [766957, 3522, 33293] C755 40) [197, 1761, 766957] C755
156) [937633, 3215, 2349648] C755 25) [37, 6425, 8438697] C755
157) [1015697, 1367, 213248] C755 21) [17, 2734, 1015697] C755
158) [1032377, 1123, 57188] C755 18) [17, 2246, 1032377] C755
159) [1250309, 1197, 45625] C755 30) [73, 2394, 1250309] C755
160) [1392697, 1835, 493632] C755 55) [857, 3670, 1392697] C755
161) [1587737, 1275, 9472] C755 23) [37, 2550, 1587737] C755
162) [1593797, 1285, 14357] C755 43) [293, 2570, 1593797] C755
163) [1596641, 2063, 664832] C755 27) [53, 4126, 1596641] C755
164) [1613069, 1313, 27725] C755 60) [1109, 2626, 1613069] C755
165) [1916749, 2337, 886205] C755 ---) [5, 2801, 1916749] C151
166) [2058713, 1435, 128] C755 ---) [8, 2870, 2058713] C151
167) [2090329, 1499, 39168] C755 ---) [17, 2998, 2090329] C151
168) [2121761, 1519, 46400] C755 22) [29, 3038, 2121761] C755
169) [2130929, 4619, 539200] C755 44) [337, 9238, 19178361] C755
170) [3212233, 1795, 2448] C755 ---) [17, 3590, 3212233] C151
171) [3269897, 2435, 664832] C755 26) [53, 4870, 3269897] C755
172) [3656753, 1991, 76832] C755 16) [8, 3982, 3656753] C755
173) [3728713, 2275, 361728] C755 36) [157, 4550, 3728713] C755
174) [3754697, 2723, 915008] C755 ---) [17, 5446, 3754697] C151
175) [5287201, 2543, 294912] C755 10) [8, 5086, 5287201] C755
176) [5519489, 2367, 20800] C755 17) [13, 4734, 5519489] C755
177) [5828401, 2951, 720000] C755 11) [8, 5902, 5828401] C755
178) [6344257, 2527, 10368] C755 7) [8, 5054, 6344257] C755
179) [6464377, 2699, 205056] C755 31) [89, 5398, 6464377] C755
180) [6964081, 2759, 162000] C755 1) [5, 5518, 6964081] C755
181) [7460449, 3407, 1036800] C755 15) [8, 6814, 7460449] C755
182) [7873009, 3047, 352800] C755 13) [8, 6094, 7873009] C755
183) [8006081, 3359, 819200] C755 14) [8, 6718, 8006081] C755
184) [10666673, 3271, 8192] C755 9) [8, 6542, 10666673] C755
185) [11025769, 3571, 431568] C755 24) [37, 7142, 11025769] C755
186) [27326569, 5267, 103680] C755 4) [5, 10534, 27326569] C755
187) [29436137, 5459, 91136] C755 32) [89, 10918, 29436137] C755
188) [30032129, 5503, 62720] C755 2) [5, 11006, 30032129] C755
189) [31989161, 5683, 76832] C755 12) [8, 11366, 31989161] C755