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 C3 x C33 non-normal (D4) quartic CM field invariants: 199 fields

K Quartic invariants Cl(OK) Igusa invariants Kr Reflex invariants Cl(OKr) Igusa invariants
1) [5, 2266, 1283509] C3 x C33 194) [1283509, 1133, 45] C3 x C33
2) [5, 2537, 1600061] C3 x C33 ---) [1600061, 2009, 609005] C3 x C3 x C99
3) [5, 1297, 413521] C3 x C33 185) [413521, 879, 89780] C3 x C33
4) [5, 2386, 1371229] C3 x C33 ---) [1371229, 1193, 13005] C3 x C3 x C33
5) [5, 2546, 1617149] C3 x C33 ---) [1617149, 1273, 845] C3 x C165
6) [5, 2077, 1060781] C3 x C33 190) [1060781, 1409, 231125] C3 x C33
7) [5, 2801, 1908869] C3 x C33 197) [1908869, 2357, 911645] C3 x C33
8) [5, 1597, 609101] C3 x C33 188) [609101, 1009, 102245] C3 x C33
9) [5, 3341, 2786789] C3 x C33 199) [2786789, 2437, 788045] C3 x C33
10) [5, 2441, 1214669] C3 x C33 193) [1214669, 2417, 1156805] C3 x C33
11) [8, 1034, 264977] C3 x C33 183) [264977, 517, 578] C3 x C33
12) [8, 1022, 149729] C3 x C33 172) [149729, 511, 27848] C3 x C33
13) [8, 1670, 680297] C3 x C33 ---) [680297, 835, 4232] C3 x C165
14) [8, 730, 72673] C3 x C33 161) [72673, 365, 15138] C3 x C33
15) [8, 830, 158113] C3 x C33 174) [158113, 415, 3528] C3 x C33
16) [8, 1522, 465833] C3 x C33 186) [465833, 761, 28322] C3 x C33
17) [8, 1990, 858953] C3 x C33 ---) [858953, 995, 32768] C3 x C3 x C33
18) [8, 2822, 1806089] C3 x C33 196) [1806089, 1411, 46208] C3 x C33
19) [8, 2278, 1292713] C3 x C33 195) [1292713, 1139, 1152] C3 x C33
20) [8, 2770, 1909513] C3 x C33 198) [1909513, 1385, 2178] C3 x C33
21) [8, 1766, 594857] C3 x C33 187) [594857, 883, 46208] C3 x C33
22) [13, 2057, 759433] C3 x C33 189) [759433, 2615, 832] C3 x C33
23) [13, 586, 85381] C3 x C33 ---) [85381, 293, 117] C3 x C825
24) [17, 4198, 1114601] C3 x C33 191) [1114601, 2099, 822800] C3 x C33
25) [17, 2102, 1094809] C3 x C33 ---) [1094809, 1051, 2448] C3 x C1353
26) [17, 3350, 1150777] C3 x C33 192) [1150777, 1675, 413712] C3 x C33
27) [37, 409, 17761] C3 x C33 133) [17761, 811, 124468] C3 x C33
28) [41, 910, 206369] C3 x C33 177) [206369, 455, 164] C3 x C33
29) [41, 770, 148061] C3 x C33 ---) [148061, 385, 41] C3 x C3 x C33
30) [53, 1029, 51001] C3 x C33 152) [51001, 1619, 30528] C3 x C33
31) [73, 3446, 908377] C3 x C33 ---) [908377, 1723, 515088] C3 x C3 x C33
32) [89, 1487, 392036] C3 x C33 168) [98009, 2974, 643025] C3 x C33
33) [109, 1597, 566725] C3 x C33 140) [22669, 1109, 165789] C3 x C33
34) [113, 843, 125428] C3 x C33 144) [31357, 1686, 208937] C3 x C33
35) [137, 1558, 177209] C3 x C33 ---) [177209, 779, 107408] C3 x C3 x C33
36) [149, 586, 37573] C3 x C33 146) [37573, 293, 12069] C3 x C33
37) [149, 1693, 17417] C3 x C33 ---) [17417, 1003, 38144] C3 x C3 x C33
38) [149, 565, 60101] C3 x C33 155) [60101, 1130, 78821] C3 x C33
39) [157, 1465, 338697] C3 x C33 147) [37633, 2155, 22608] C3 x C33
40) [157, 2302, 417969] C3 x C33 150) [46441, 1151, 226708] C3 x C33
41) [173, 2506, 41381] C3 x C33 ---) [41381, 1253, 382157] C3 x C3 x C33
42) [229, 826, 59733] C3 x C33 116) [6637, 413, 27709] C3 x C33
43) [229, 562, 56061] C3 x C33 ---) [6229, 281, 5725] C33
44) [229, 514, 65133] C3 x C33 ---) [7237, 257, 229] C33
45) [229, 413, 12357] C3 x C33 77) [1373, 381, 27709] C3 x C33
46) [233, 875, 160592] C3 x C33 126) [10037, 1345, 28193] C3 x C33
47) [257, 935, 64292] C3 x C33 ---) [16073, 1870, 617057] C33
48) [257, 1307, 203408] C3 x C33 ---) [12713, 1319, 50372] C33
49) [257, 98, 1373] C3 x C33 76) [1373, 49, 257] C3 x C33
50) [257, 263, 2836] C3 x C33 ---) [709, 369, 12593] C33
51) [269, 1802, 810725] C3 x C33 145) [32429, 901, 269] C3 x C33
52) [293, 437, 26573] C3 x C33 ---) [26573, 874, 84677] C3 x C3 x C99
53) [313, 787, 132228] C3 x C33 100) [3673, 895, 45072] C3 x C33
54) [317, 1573, 395969] C3 x C33 121) [8081, 1051, 31700] C3 x C33
55) [317, 289, 3049] C3 x C33 97) [3049, 578, 71325] C3 x C33
56) [353, 935, 218468] C3 x C33 153) [54617, 1870, 353] C3 x C33
57) [397, 1517, 17041] C3 x C33 130) [17041, 2587, 1157652] C3 x C33
58) [433, 4419, 3985472] C3 x C33 156) [62273, 3051, 443392] C3 x C33
59) [557, 574, 2161] C3 x C33 87) [2161, 287, 20052] C3 x C33
60) [613, 1453, 159849] C3 x C33 132) [17761, 2906, 1471813] C3 x C33
61) [677, 165, 6637] C3 x C33 ---) [6637, 330, 677] C3 x C3 x C33
62) [733, 986, 5557] C3 x C33 ---) [5557, 493, 59373] C33
63) [733, 397, 8433] C3 x C33 ---) [937, 794, 123877] C33
64) [733, 445, 27333] C3 x C33 ---) [3037, 890, 88693] C33
65) [733, 141, 389] C3 x C33 ---) [389, 282, 18325] C33
66) [733, 442, 45909] C3 x C33 ---) [5101, 221, 733] C33
67) [761, 1427, 219712] C3 x C33 ---) [3433, 1611, 194816] C33
68) [761, 583, 16292] C3 x C33 ---) [4073, 1166, 274721] C33
69) [761, 415, 20036] C3 x C33 ---) [5009, 830, 92081] C33
70) [857, 979, 126272] C3 x C33 85) [1973, 865, 103697] C3 x C33
71) [941, 1333, 272725] C3 x C33 ---) [10909, 2666, 685989] C3 x C165
72) [941, 2338, 7757] C3 x C33 120) [7757, 1169, 339701] C3 x C33
73) [941, 529, 69725] C3 x C33 94) [2789, 1058, 941] C3 x C33
74) [1153, 547, 72208] C3 x C33 104) [4513, 1094, 10377] C3 x C33
75) [1229, 529, 829] C3 x C33 ---) [829, 1058, 276525] C33
76) [1373, 49, 257] C3 x C33 49) [257, 98, 1373] C3 x C33
77) [1373, 381, 27709] C3 x C33 45) [229, 413, 12357] C3 x C33
78) [1409, 1979, 970304] C3 x C33 129) [15161, 3958, 35225] C3 x C33
79) [1489, 1063, 85572] C3 x C33 ---) [2377, 1703, 291844] C33
80) [1489, 1066, 135189] C3 x C33 ---) [1669, 533, 37225] C33
81) [1489, 935, 21636] C3 x C33 ---) [601, 479, 53604] C33
82) [1733, 717, 3313] C3 x C33 98) [3313, 1434, 500837] C3 x C33
83) [1889, 814, 135425] C3 x C33 ---) [5417, 407, 7556] C3 x C231
84) [1901, 229, 8833] C3 x C33 ---) [73, 303, 7604] C33
85) [1973, 865, 103697] C3 x C33 70) [857, 979, 126272] C3 x C33
86) [2137, 1802, 119413] C3 x C33 90) [2437, 901, 173097] C3 x C33
87) [2161, 287, 20052] C3 x C33 59) [557, 574, 2161] C3 x C33
88) [2221, 626, 18013] C3 x C33 134) [18013, 313, 19989] C3 x C33
89) [2377, 2199, 1136996] C3 x C33 112) [5801, 3147, 38032] C3 x C33
90) [2437, 901, 173097] C3 x C33 86) [2137, 1802, 119413] C3 x C33
91) [2633, 2638, 1360609] C3 x C33 102) [3769, 1319, 94788] C3 x C33
92) [2677, 161, 457] C3 x C33 ---) [457, 322, 24093] C33
93) [2713, 210, 173] C3 x C33 ---) [173, 105, 2713] C33
94) [2789, 1058, 941] C3 x C33 73) [941, 529, 69725] C3 x C33
95) [2917, 1153, 69093] C3 x C33 ---) [853, 1297, 26253] C33
96) [2953, 2027, 565776] C3 x C33 103) [3929, 3759, 3413668] C3 x C33
97) [3049, 578, 71325] C3 x C33 55) [317, 289, 3049] C3 x C33
98) [3313, 1434, 500837] C3 x C33 82) [1733, 717, 3313] C3 x C33
99) [3533, 1357, 452413] C3 x C33 ---) [2677, 2714, 31797] C3 x C3 x C33
100) [3673, 895, 45072] C3 x C33 53) [313, 787, 132228] C3 x C33
101) [3673, 1247, 365796] C3 x C33 ---) [1129, 2147, 528912] C3 x C3 x C99
102) [3769, 1319, 94788] C3 x C33 91) [2633, 2638, 1360609] C3 x C33
103) [3929, 3759, 3413668] C3 x C33 96) [2953, 2027, 565776] C3 x C33
104) [4513, 1094, 10377] C3 x C33 74) [1153, 547, 72208] C3 x C33
105) [4597, 69, 41] C3 x C33 ---) [41, 138, 4597] C33
106) [4597, 889, 3357] C3 x C33 ---) [373, 965, 225253] C33
107) [4649, 1022, 186737] C3 x C33 ---) [353, 511, 18596] C33
108) [4933, 109, 1737] C3 x C33 ---) [193, 218, 4933] C33
109) [5209, 2078, 329425] C3 x C33 128) [13177, 1039, 187524] C3 x C33
110) [5333, 77, 149] C3 x C33 ---) [149, 154, 5333] C33
111) [5741, 410, 19061] C3 x C33 ---) [389, 205, 5741] C33
112) [5801, 3147, 38032] C3 x C33 89) [2377, 2199, 1136996] C3 x C33
113) [6133, 1201, 175077] C3 x C33 ---) [397, 1265, 6133] C33
114) [6133, 313, 10693] C3 x C33 ---) [37, 517, 6133] C33
115) [6133, 305, 9457] C3 x C33 ---) [193, 610, 55197] C33
116) [6637, 413, 27709] C3 x C33 42) [229, 826, 59733] C3 x C33
117) [7481, 1363, 372800] C3 x C33 ---) [233, 739, 119696] C33
118) [7481, 570, 51301] C3 x C33 ---) [61, 285, 7481] C33
119) [7673, 171, 5392] C3 x C33 ---) [337, 342, 7673] C33
120) [7757, 1169, 339701] C3 x C33 72) [941, 2338, 7757] C3 x C33
121) [8081, 1051, 31700] C3 x C33 54) [317, 1573, 395969] C3 x C33
122) [8581, 289, 1573] C3 x C33 ---) [13, 193, 8581] C33
123) [8597, 562, 44573] C3 x C33 ---) [53, 281, 8597] C33
124) [9133, 121, 1377] C3 x C33 ---) [17, 242, 9133] C33
125) [9749, 157, 3725] C3 x C33 ---) [149, 314, 9749] C33
126) [10037, 1345, 28193] C3 x C33 46) [233, 875, 160592] C3 x C33
127) [12197, 474, 7381] C3 x C33 ---) [61, 237, 12197] C33
128) [13177, 1039, 187524] C3 x C33 109) [5209, 2078, 329425] C3 x C33
129) [15161, 3958, 35225] C3 x C33 78) [1409, 1979, 970304] C3 x C33
130) [17041, 2587, 1157652] C3 x C33 57) [397, 1517, 17041] C3 x C33
131) [17053, 185, 4293] C3 x C33 ---) [53, 370, 17053] C33
132) [17761, 2906, 1471813] C3 x C33 60) [613, 1453, 159849] C3 x C33
133) [17761, 811, 124468] C3 x C33 27) [37, 409, 17761] C3 x C33
134) [18013, 313, 19989] C3 x C33 88) [2221, 626, 18013] C3 x C33
135) [18521, 2911, 2002724] C3 x C33 ---) [521, 2251, 1185344] C33
136) [18701, 137, 17] C3 x C33 ---) [17, 274, 18701] C33
137) [20297, 483, 53248] C3 x C33 ---) [13, 321, 20297] C33
138) [20521, 179, 2880] C3 x C33 ---) [5, 297, 20521] C33
139) [20549, 157, 1025] C3 x C33 ---) [41, 314, 20549] C33
140) [22669, 1109, 165789] C3 x C33 33) [109, 1597, 566725] C3 x C33
141) [23297, 157, 338] C3 x C33 ---) [8, 314, 23297] C33
142) [23297, 1243, 240656] C3 x C33 ---) [89, 839, 93188] C33
143) [24533, 157, 29] C3 x C33 ---) [29, 314, 24533] C33
144) [31357, 1686, 208937] C3 x C33 34) [113, 843, 125428] C3 x C33
145) [32429, 901, 269] C3 x C33 51) [269, 1802, 810725] C3 x C33
146) [37573, 293, 12069] C3 x C33 36) [149, 586, 37573] C3 x C33
147) [37633, 2155, 22608] C3 x C33 39) [157, 1465, 338697] C3 x C33
148) [42649, 211, 468] C3 x C33 ---) [13, 422, 42649] C33
149) [43961, 259, 5780] C3 x C33 ---) [5, 437, 43961] C33
150) [46441, 1151, 226708] C3 x C33 40) [157, 2302, 417969] C3 x C33
151) [46489, 647, 52] C3 x C33 ---) [13, 509, 46489] C33
152) [51001, 1619, 30528] C3 x C33 30) [53, 1029, 51001] C3 x C33
153) [54617, 1870, 353] C3 x C33 56) [353, 935, 218468] C3 x C33
154) [58061, 241, 5] C3 x C33 ---) [5, 482, 58061] C33
155) [60101, 1130, 78821] C3 x C33 38) [149, 565, 60101] C3 x C33
156) [62273, 3051, 443392] C3 x C33 58) [433, 4419, 3985472] C3 x C33
157) [62929, 271, 2628] C3 x C33 ---) [73, 542, 62929] C33
158) [64489, 259, 648] C3 x C33 ---) [8, 518, 64489] C33
159) [71329, 303, 5120] C3 x C33 ---) [5, 589, 71329] C33
160) [71741, 281, 1805] C3 x C33 ---) [5, 562, 71741] C33
161) [72673, 365, 15138] C3 x C33 14) [8, 730, 72673] C3 x C33
162) [85621, 1410, 154541] C3 x C33 ---) [29, 705, 85621] C33
163) [87041, 1531, 41984] C3 x C33 ---) [41, 1391, 348164] C33
164) [89657, 347, 7688] C3 x C33 ---) [8, 694, 89657] C33
165) [92269, 433, 23805] C3 x C33 ---) [5, 609, 92269] C33
166) [92581, 501, 39605] C3 x C33 ---) [5, 613, 92581] C33
167) [96457, 387, 13328] C3 x C33 ---) [17, 774, 96457] C33
168) [98009, 2974, 643025] C3 x C33 32) [89, 1487, 392036] C3 x C33
169) [108649, 1043, 244800] C3 x C33 ---) [17, 1319, 434596] C33
170) [119321, 347, 272] C3 x C33 ---) [17, 694, 119321] C33
171) [131797, 1145, 31213] C3 x C33 ---) [13, 749, 131797] C33
172) [149729, 511, 27848] C3 x C33 12) [8, 1022, 149729] C3 x C33
173) [157141, 397, 117] C3 x C33 ---) [13, 794, 157141] C33
174) [158113, 415, 3528] C3 x C33 15) [8, 830, 158113] C3 x C33
175) [165541, 421, 2925] C3 x C33 ---) [13, 842, 165541] C33
176) [170389, 413, 45] C3 x C33 ---) [5, 826, 170389] C33
177) [206369, 455, 164] C3 x C33 28) [41, 910, 206369] C3 x C33
178) [209189, 853, 129605] C3 x C33 ---) [5, 949, 209189] C33
179) [211349, 877, 139445] C3 x C33 ---) [5, 961, 211349] C33
180) [220589, 737, 80645] C3 x C33 ---) [5, 941, 220589] C33
181) [245849, 593, 26450] C3 x C33 ---) [8, 1186, 245849] C33
182) [246509, 497, 125] C3 x C33 ---) [5, 994, 246509] C33
183) [264977, 517, 578] C3 x C33 11) [8, 1034, 264977] C3 x C33
184) [304709, 773, 73205] C3 x C33 ---) [5, 1109, 304709] C33
185) [413521, 879, 89780] C3 x C33 3) [5, 1297, 413521] C3 x C33
186) [465833, 761, 28322] C3 x C33 16) [8, 1522, 465833] C3 x C33
187) [594857, 883, 46208] C3 x C33 21) [8, 1766, 594857] C3 x C33
188) [609101, 1009, 102245] C3 x C33 8) [5, 1597, 609101] C3 x C33
189) [759433, 2615, 832] C3 x C33 22) [13, 2057, 759433] C3 x C33
190) [1060781, 1409, 231125] C3 x C33 6) [5, 2077, 1060781] C3 x C33
191) [1114601, 2099, 822800] C3 x C33 24) [17, 4198, 1114601] C3 x C33
192) [1150777, 1675, 413712] C3 x C33 26) [17, 3350, 1150777] C3 x C33
193) [1214669, 2417, 1156805] C3 x C33 10) [5, 2441, 1214669] C3 x C33
194) [1283509, 1133, 45] C3 x C33 1) [5, 2266, 1283509] C3 x C33
195) [1292713, 1139, 1152] C3 x C33 19) [8, 2278, 1292713] C3 x C33
196) [1806089, 1411, 46208] C3 x C33 18) [8, 2822, 1806089] C3 x C33
197) [1908869, 2357, 911645] C3 x C33 7) [5, 2801, 1908869] C3 x C33
198) [1909513, 1385, 2178] C3 x C33 20) [8, 2770, 1909513] C3 x C33
199) [2786789, 2437, 788045] C3 x C33 9) [5, 3341, 2786789] C3 x C33