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 C5 x C10 non-normal (D4) quartic CM field invariants: 181 fields

K Quartic invariants Cl(OK) Igusa invariants Kr Reflex invariants Cl(OKr) Igusa invariants
1) [5, 152, 4931] C5 x C10 148) [19724, 304, 3380] C5 x C10
2) [5, 1381, 461389] C5 x C10 178) [461389, 897, 85805] C5 x C10
3) [5, 1045, 268045] C5 x C10 ---) [268045, 705, 57245] C5 x C40
4) [5, 1137, 262141] C5 x C10 175) [262141, 1129, 253125] C5 x C10
5) [5, 601, 79489] C5 x C10 ---) [79489, 567, 60500] C10 x C10
6) [5, 1474, 515789] C5 x C10 179) [515789, 737, 6845] C5 x C10
7) [5, 1269, 364309] C5 x C10 ---) [364309, 733, 43245] C5 x C30
8) [5, 1401, 439189] C5 x C10 ---) [439189, 797, 49005] C5 x C70
9) [8, 1426, 508169] C5 x C10 ---) [508169, 713, 50] C5 x C20
10) [8, 1798, 775433] C5 x C10 ---) [775433, 899, 8192] C10 x C10
11) [8, 196, 5906] C5 x C10 ---) [23624, 196, 3698] C5 x C40
12) [8, 1618, 409481] C5 x C10 176) [409481, 809, 61250] C5 x C10
13) [8, 1222, 327113] C5 x C10 ---) [327113, 611, 11552] C10 x C10
14) [8, 1078, 197209] C5 x C10 170) [197209, 539, 23328] C5 x C10
15) [8, 1110, 268825] C5 x C10 136) [10753, 555, 9800] C5 x C10
16) [8, 1090, 274553] C5 x C10 ---) [274553, 545, 5618] C5 x C40
17) [12, 458, 39373] C5 x C10 158) [39373, 229, 3267] C5 x C10
18) [12, 1170, 145617] C5 x C10 165) [145617, 585, 49152] C5 x C10
19) [12, 1334, 437977] C5 x C10 177) [437977, 667, 1728] C5 x C10
20) [12, 998, 248809] C5 x C10 174) [248809, 499, 48] C5 x C10
21) [12, 1114, 94777] C5 x C10 162) [94777, 557, 53868] C5 x C10
22) [12, 1814, 803449] C5 x C10 181) [803449, 907, 4800] C5 x C10
23) [12, 152, 5413] C5 x C10 124) [5413, 238, 8748] C5 x C10
24) [12, 698, 39133] C5 x C10 157) [39133, 349, 20667] C5 x C10
25) [12, 1490, 554257] C5 x C10 180) [554257, 745, 192] C5 x C10
26) [12, 790, 149113] C5 x C10 166) [149113, 395, 1728] C5 x C10
27) [13, 272, 14284] C5 x C10 141) [14284, 136, 1053] C5 x C10
28) [13, 227, 12619] C5 x C10 ---) [50476, 454, 1053] C5 x C130
29) [17, 397, 39398] C5 x C10 168) [157592, 794, 17] C5 x C10
30) [17, 724, 59219] C5 x C10 172) [236876, 1448, 287300] C5 x C10
31) [21, 745, 34381] C5 x C10 155) [34381, 573, 4725] C5 x C10
32) [21, 1034, 65605] C5 x C10 ---) [65605, 517, 50421] C5 x C20
33) [24, 2012, 850660] C5 x C10 ---) [212665, 1006, 40344] C5 x C20
34) [28, 1744, 708612] C5 x C10 169) [177153, 872, 12943] C5 x C10
35) [28, 864, 186596] C5 x C10 ---) [46649, 432, 7] C5 x C90
36) [29, 685, 103901] C5 x C10 164) [103901, 1370, 53621] C5 x C10
37) [29, 733, 109085] C5 x C10 ---) [109085, 1466, 100949] C10 x C10
38) [29, 498, 61885] C5 x C10 ---) [61885, 249, 29] C10 x C10
39) [29, 649, 98333] C5 x C10 163) [98333, 1298, 27869] C5 x C10
40) [33, 353, 30154] C5 x C10 ---) [120616, 706, 3993] C5 x C20
41) [33, 1286, 242377] C5 x C10 173) [242377, 643, 42768] C5 x C10
42) [33, 560, 50647] C5 x C10 171) [202588, 1120, 111012] C5 x C10
43) [37, 1525, 497925] C5 x C10 ---) [2213, 825, 156325] C5 x C30
44) [37, 557, 76813] C5 x C10 161) [76813, 1114, 2997] C5 x C10
45) [41, 389, 37574] C5 x C10 167) [150296, 778, 1025] C5 x C10
46) [41, 537, 36412] C5 x C10 156) [36412, 1074, 142721] C5 x C10
47) [44, 70, 1126] C5 x C10 ---) [4504, 140, 396] C5 x C5 x C10
48) [44, 328, 23332] C5 x C10 126) [5833, 164, 891] C5 x C10
49) [53, 553, 27149] C5 x C10 ---) [27149, 1106, 197213] C5 x C40
50) [56, 710, 82121] C5 x C10 ---) [82121, 355, 10976] C5 x C40
51) [57, 314, 13477] C5 x C10 139) [13477, 157, 2793] C5 x C10
52) [61, 1549, 398169] C5 x C10 159) [44241, 1139, 47824] C5 x C10
53) [77, 282, 12181] C5 x C10 ---) [12181, 141, 1925] C5 x C80
54) [88, 1306, 394641] C5 x C10 ---) [43849, 653, 7942] C5 x C20
55) [93, 209, 10897] C5 x C10 ---) [10897, 418, 93] C5 x C20
56) [113, 217, 8354] C5 x C10 ---) [33416, 434, 13673] C5 x C80
57) [129, 542, 71377] C5 x C10 ---) [71377, 271, 516] C5 x C20
58) [129, 512, 8647] C5 x C10 ---) [34588, 1024, 227556] C5 x C130
59) [129, 436, 37075] C5 x C10 127) [5932, 872, 41796] C5 x C10
60) [181, 466, 18813] C5 x C10 147) [18813, 233, 8869] C5 x C10
61) [188, 422, 17449] C5 x C10 146) [17449, 211, 6768] C5 x C10
62) [217, 823, 28228] C5 x C10 ---) [7057, 1255, 250852] C5 x C210
63) [301, 2306, 18253] C5 x C10 ---) [18253, 1153, 327789] C5 x C5 x C10
64) [313, 775, 136932] C5 x C10 154) [34233, 1550, 52897] C5 x C10
65) [353, 535, 46052] C5 x C10 ---) [11513, 1070, 102017] C5 x C40
66) [381, 661, 29125] C5 x C10 ---) [1165, 353, 30861] C5 x C20
67) [401, 123, 2880] C5 x C10 ---) [5, 129, 3609] C10
68) [412, 752, 131076] C5 x C10 117) [3641, 376, 2575] C5 x C10
69) [428, 74, 941] C5 x C10 87) [941, 37, 107] C5 x C10
70) [449, 329, 26050] C5 x C10 ---) [4168, 658, 4041] C5 x C40
71) [449, 254, 8945] C5 x C10 ---) [8945, 127, 1796] C5 x C40
72) [472, 698, 15601] C5 x C10 143) [15601, 349, 26550] C5 x C10
73) [517, 421, 44181] C5 x C10 123) [4909, 842, 517] C5 x C10
74) [541, 1074, 234269] C5 x C10 121) [4781, 537, 13525] C5 x C10
75) [553, 839, 115012] C5 x C10 153) [28753, 1678, 243873] C5 x C10
76) [581, 730, 75125] C5 x C10 ---) [3005, 365, 14525] C5 x C20
77) [593, 1015, 8348] C5 x C10 134) [8348, 2030, 996833] C5 x C10
78) [649, 929, 214300] C5 x C10 ---) [8572, 1858, 5841] C5 x C30
79) [653, 1153, 245993] C5 x C10 107) [2033, 595, 2612] C5 x C10
80) [669, 393, 25065] C5 x C10 ---) [2785, 786, 54189] C5 x C20
81) [673, 686, 20737] C5 x C10 ---) [20737, 343, 24228] C5 x C5 x C40
82) [709, 301, 22473] C5 x C10 110) [2497, 602, 709] C5 x C10
83) [757, 154, 2901] C5 x C10 112) [2901, 77, 757] C5 x C10
84) [769, 1270, 206361] C5 x C10 150) [22929, 635, 49216] C5 x C10
85) [817, 803, 12304] C5 x C10 ---) [769, 583, 29412] C10
86) [829, 1362, 62525] C5 x C10 ---) [2501, 681, 100309] C5 x C40
87) [941, 37, 107] C5 x C10 69) [428, 74, 941] C5 x C10
88) [1004, 398, 3457] C5 x C10 115) [3457, 199, 9036] C5 x C10
89) [1077, 453, 29493] C5 x C10 ---) [3277, 906, 87237] C5 x C20
90) [1093, 41, 147] C5 x C10 ---) [12, 82, 1093] C10
91) [1093, 250, 11253] C5 x C10 ---) [93, 125, 1093] C10
92) [1141, 997, 97605] C5 x C10 ---) [1205, 1021, 192829] C5 x C20
93) [1361, 692, 9475] C5 x C10 98) [1516, 1384, 440964] C5 x C10
94) [1393, 319, 25092] C5 x C10 ---) [697, 638, 1393] C60
95) [1401, 815, 123676] C5 x C10 111) [2524, 1630, 169521] C5 x C10
96) [1429, 241, 5589] C5 x C10 ---) [69, 221, 1429] C10
97) [1429, 341, 133] C5 x C10 ---) [133, 349, 12861] C10
98) [1516, 1384, 440964] C5 x C10 93) [1361, 692, 9475] C5 x C10
99) [1589, 178, 1565] C5 x C10 ---) [1565, 89, 1589] C5 x C20
100) [1641, 41, 10] C5 x C10 ---) [40, 82, 1641] C20
101) [1756, 542, 10225] C5 x C10 ---) [409, 271, 15804] C10
102) [1897, 178, 333] C5 x C10 ---) [37, 89, 1897] C10
103) [1996, 98, 405] C5 x C10 ---) [5, 49, 499] C10
104) [1996, 328, 24900] C5 x C10 ---) [249, 164, 499] C10
105) [1996, 136, 2628] C5 x C10 ---) [73, 68, 499] C10
106) [1996, 70, 726] C5 x C10 ---) [24, 86, 499] C10
107) [2033, 595, 2612] C5 x C10 79) [653, 1153, 245993] C5 x C10
108) [2441, 1003, 221600] C5 x C10 ---) [2216, 2006, 119609] C10 x C10
109) [2476, 2616, 1153764] C5 x C10 116) [3561, 1308, 139275] C5 x C10
110) [2497, 602, 709] C5 x C10 82) [709, 301, 22473] C5 x C10
111) [2524, 1630, 169521] C5 x C10 95) [1401, 815, 123676] C5 x C10
112) [2901, 77, 757] C5 x C10 83) [757, 154, 2901] C5 x C10
113) [2908, 336, 2052] C5 x C10 ---) [57, 168, 6543] C10
114) [3292, 238, 993] C5 x C10 ---) [993, 119, 3292] C5 x C30
115) [3457, 199, 9036] C5 x C10 88) [1004, 398, 3457] C5 x C10
116) [3561, 1308, 139275] C5 x C10 109) [2476, 2616, 1153764] C5 x C10
117) [3641, 376, 2575] C5 x C10 68) [412, 752, 131076] C5 x C10
118) [3676, 4334, 1387489] C5 x C10 122) [4801, 2167, 827100] C5 x C10
119) [3901, 1005, 228125] C5 x C10 ---) [365, 909, 191149] C5 x C20
120) [3928, 138, 833] C5 x C10 ---) [17, 69, 982] C10
121) [4781, 537, 13525] C5 x C10 74) [541, 1074, 234269] C5 x C10
122) [4801, 2167, 827100] C5 x C10 118) [3676, 4334, 1387489] C5 x C10
123) [4909, 842, 517] C5 x C10 73) [517, 421, 44181] C5 x C10
124) [5413, 238, 8748] C5 x C10 23) [12, 152, 5413] C5 x C10
125) [5793, 489, 46746] C5 x C10 ---) [424, 978, 52137] C5 x C20
126) [5833, 164, 891] C5 x C10 48) [44, 328, 23332] C5 x C10
127) [5932, 872, 41796] C5 x C10 59) [129, 436, 37075] C5 x C10
128) [6481, 232, 6975] C5 x C10 ---) [124, 464, 25924] C10
129) [7064, 266, 10625] C5 x C10 ---) [17, 133, 1766] C10
130) [7513, 91, 192] C5 x C10 ---) [12, 182, 7513] C10
131) [7513, 263, 388] C5 x C10 ---) [97, 526, 67617] C10
132) [7649, 93, 250] C5 x C10 ---) [40, 186, 7649] C10 x C10
133) [8108, 280, 11492] C5 x C10 ---) [17, 140, 2027] C10
134) [8348, 2030, 996833] C5 x C10 77) [593, 1015, 8348] C5 x C10
135) [8689, 395, 19456] C5 x C10 ---) [76, 790, 78201] C10
136) [10753, 555, 9800] C5 x C10 15) [8, 1110, 268825] C5 x C10
137) [12061, 589, 11349] C5 x C10 ---) [1261, 1178, 301525] C5 x C20
138) [13349, 117, 85] C5 x C10 ---) [85, 234, 13349] C5 x C20
139) [13477, 157, 2793] C5 x C10 51) [57, 314, 13477] C5 x C10
140) [13953, 611, 61936] C5 x C10 ---) [316, 1222, 125577] C5 x C30
141) [14284, 136, 1053] C5 x C10 27) [13, 272, 14284] C5 x C10
142) [15121, 127, 252] C5 x C10 ---) [28, 254, 15121] C10
143) [15601, 349, 26550] C5 x C10 72) [472, 698, 15601] C5 x C10
144) [15889, 367, 29700] C5 x C10 ---) [33, 734, 15889] C10
145) [15989, 253, 12005] C5 x C10 ---) [5, 269, 15989] C10
146) [17449, 211, 6768] C5 x C10 61) [188, 422, 17449] C5 x C10
147) [18813, 233, 8869] C5 x C10 60) [181, 466, 18813] C5 x C10
148) [19724, 304, 3380] C5 x C10 1) [5, 152, 4931] C5 x C10
149) [20953, 145, 18] C5 x C10 ---) [8, 290, 20953] C10
150) [22929, 635, 49216] C5 x C10 84) [769, 1270, 206361] C5 x C10
151) [24241, 159, 260] C5 x C10 ---) [65, 318, 24241] C5 x C20
152) [27929, 177, 850] C5 x C10 ---) [136, 354, 27929] C5 x C20
153) [28753, 1678, 243873] C5 x C10 75) [553, 839, 115012] C5 x C10
154) [34233, 1550, 52897] C5 x C10 64) [313, 775, 136932] C5 x C10
155) [34381, 573, 4725] C5 x C10 31) [21, 745, 34381] C5 x C10
156) [36412, 1074, 142721] C5 x C10 46) [41, 537, 36412] C5 x C10
157) [39133, 349, 20667] C5 x C10 24) [12, 698, 39133] C5 x C10
158) [39373, 229, 3267] C5 x C10 17) [12, 458, 39373] C5 x C10
159) [44241, 1139, 47824] C5 x C10 52) [61, 1549, 398169] C5 x C10
160) [51433, 265, 4698] C5 x C10 ---) [232, 530, 51433] C5 x C20
161) [76813, 1114, 2997] C5 x C10 44) [37, 557, 76813] C5 x C10
162) [94777, 557, 53868] C5 x C10 21) [12, 1114, 94777] C5 x C10
163) [98333, 1298, 27869] C5 x C10 39) [29, 649, 98333] C5 x C10
164) [103901, 1370, 53621] C5 x C10 36) [29, 685, 103901] C5 x C10
165) [145617, 585, 49152] C5 x C10 18) [12, 1170, 145617] C5 x C10
166) [149113, 395, 1728] C5 x C10 26) [12, 790, 149113] C5 x C10
167) [150296, 778, 1025] C5 x C10 45) [41, 389, 37574] C5 x C10
168) [157592, 794, 17] C5 x C10 29) [17, 397, 39398] C5 x C10
169) [177153, 872, 12943] C5 x C10 34) [28, 1744, 708612] C5 x C10
170) [197209, 539, 23328] C5 x C10 14) [8, 1078, 197209] C5 x C10
171) [202588, 1120, 111012] C5 x C10 42) [33, 560, 50647] C5 x C10
172) [236876, 1448, 287300] C5 x C10 30) [17, 724, 59219] C5 x C10
173) [242377, 643, 42768] C5 x C10 41) [33, 1286, 242377] C5 x C10
174) [248809, 499, 48] C5 x C10 20) [12, 998, 248809] C5 x C10
175) [262141, 1129, 253125] C5 x C10 4) [5, 1137, 262141] C5 x C10
176) [409481, 809, 61250] C5 x C10 12) [8, 1618, 409481] C5 x C10
177) [437977, 667, 1728] C5 x C10 19) [12, 1334, 437977] C5 x C10
178) [461389, 897, 85805] C5 x C10 2) [5, 1381, 461389] C5 x C10
179) [515789, 737, 6845] C5 x C10 6) [5, 1474, 515789] C5 x C10
180) [554257, 745, 192] C5 x C10 25) [12, 1490, 554257] C5 x C10
181) [803449, 907, 4800] C5 x C10 22) [12, 1814, 803449] C5 x C10