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 C21 non-normal (D4) quartic CM field invariants: 200 fields

K Quartic invariants Cl(OK) Igusa invariants Kr Reflex invariants Cl(OKr) Igusa invariants
1) [5, 821, 164449] C3 x C21 178) [164449, 687, 76880] C3 x C21
2) [5, 1457, 529181] C3 x C21 194) [529181, 1049, 142805] C3 x C21
3) [5, 1389, 409729] C3 x C21 188) [409729, 1343, 348480] C3 x C21
4) [5, 1094, 245129] C3 x C21 182) [245129, 547, 13520] C3 x C21
5) [5, 821, 168409] C3 x C21 179) [168409, 627, 56180] C3 x C21
6) [5, 1618, 564701] C3 x C21 195) [564701, 809, 22445] C3 x C21
7) [5, 2081, 1082189] C3 x C21 198) [1082189, 1537, 320045] C3 x C21
8) [5, 2186, 1014149] C3 x C21 ---) [1014149, 1093, 45125] C3 x C3 x C21
9) [5, 901, 202889] C3 x C21 180) [202889, 667, 60500] C3 x C21
10) [5, 1746, 672349] C3 x C21 196) [672349, 873, 22445] C3 x C21
11) [5, 993, 229981] C3 x C21 181) [229981, 601, 32805] C3 x C21
12) [5, 2261, 1252469] C3 x C21 199) [1252469, 1517, 262205] C3 x C21
13) [5, 1322, 388901] C3 x C21 ---) [388901, 661, 12005] C3 x C3 x C21
14) [5, 1321, 430649] C3 x C21 189) [430649, 907, 98000] C3 x C21
15) [5, 1297, 368021] C3 x C21 185) [368021, 1229, 285605] C3 x C21
16) [5, 1221, 344209] C3 x C21 184) [344209, 727, 46080] C3 x C21
17) [5, 758, 117721] C3 x C21 174) [117721, 379, 6480] C3 x C21
18) [8, 2434, 1268537] C3 x C21 200) [1268537, 1217, 53138] C3 x C21
19) [8, 2018, 773081] C3 x C21 ---) [773081, 1009, 61250] C3 x C3 x C21
20) [8, 634, 68737] C3 x C21 163) [68737, 317, 7938] C3 x C21
21) [8, 1270, 378137] C3 x C21 187) [378137, 635, 6272] C3 x C21
22) [8, 1218, 369913] C3 x C21 186) [369913, 609, 242] C3 x C21
23) [8, 1986, 497977] C3 x C21 191) [497977, 993, 122018] C3 x C21
24) [8, 558, 50929] C3 x C21 155) [50929, 279, 6728] C3 x C21
25) [8, 1718, 411449] C3 x C21 ---) [411449, 859, 81608] C3 x C3 x C21
26) [8, 2150, 848297] C3 x C21 197) [848297, 1075, 76832] C3 x C21
27) [8, 682, 101489] C3 x C21 172) [101489, 341, 3698] C3 x C21
28) [13, 1466, 514357] C3 x C21 192) [514357, 733, 5733] C3 x C21
29) [13, 597, 69833] C3 x C21 165) [69833, 891, 181012] C3 x C21
30) [13, 1733, 732541] C3 x C21 ---) [732541, 2789, 296413] C3 x C3 x C21
31) [13, 1050, 204437] C3 x C21 ---) [204437, 525, 17797] C3 x C105
32) [13, 1514, 516421] C3 x C21 193) [516421, 757, 14157] C3 x C21
33) [29, 653, 63617] C3 x C21 162) [63617, 1306, 171941] C3 x C21
34) [29, 453, 30937] C3 x C21 144) [30937, 906, 81461] C3 x C21
35) [29, 686, 71249] C3 x C21 166) [71249, 343, 11600] C3 x C21
36) [37, 537, 71861] C3 x C21 ---) [71861, 1074, 925] C3 x C3 x C21
37) [41, 2815, 1942916] C3 x C21 190) [485729, 3851, 671744] C3 x C21
38) [41, 2039, 1025348] C3 x C21 183) [256337, 2771, 317504] C3 x C21
39) [41, 578, 24317] C3 x C21 139) [24317, 289, 14801] C3 x C21
40) [41, 1255, 166196] C3 x C21 151) [41549, 857, 173225] C3 x C21
41) [53, 437, 43913] C3 x C21 152) [43913, 874, 15317] C3 x C21
42) [61, 810, 75941] C3 x C21 167) [75941, 405, 22021] C3 x C21
43) [73, 555, 36692] C3 x C21 121) [9173, 741, 134977] C3 x C21
44) [101, 409, 41189] C3 x C21 150) [41189, 818, 2525] C3 x C21
45) [137, 482, 13693] C3 x C21 ---) [13693, 241, 11097] C3 x C3 x C105
46) [137, 447, 37588] C3 x C21 123) [9397, 894, 49457] C3 x C21
47) [157, 2533, 429309] C3 x C21 ---) [47701, 1481, 441013] C3 x C3 x C21
48) [173, 1258, 29573] C3 x C21 143) [29573, 629, 91517] C3 x C21
49) [173, 538, 38453] C3 x C21 149) [38453, 269, 8477] C3 x C21
50) [229, 154, 5013] C3 x C21 ---) [557, 77, 229] C21
51) [229, 221, 7573] C3 x C21 ---) [7573, 442, 18549] C3 x C63
52) [229, 745, 60381] C3 x C21 ---) [6709, 1229, 229] C21
53) [229, 281, 19225] C3 x C21 ---) [769, 355, 8244] C21
54) [233, 2003, 454928] C3 x C21 142) [28433, 1655, 336452] C3 x C21
55) [241, 1475, 499984] C3 x C21 146) [31249, 2687, 47236] C3 x C21
56) [241, 1462, 148761] C3 x C21 131) [16529, 731, 96400] C3 x C21
57) [257, 295, 3188] C3 x C21 ---) [797, 481, 257] C21
58) [257, 499, 39056] C3 x C21 ---) [2441, 631, 25700] C21
59) [257, 158, 2129] C3 x C21 ---) [2129, 79, 1028] C21
60) [269, 481, 15809] C3 x C21 ---) [15809, 962, 168125] C21 x C21
61) [281, 2262, 991417] C3 x C21 135) [20233, 1131, 71936] C3 x C21
62) [281, 790, 138041] C3 x C21 175) [138041, 395, 4496] C3 x C21
63) [293, 205, 6917] C3 x C21 120) [6917, 410, 14357] C3 x C21
64) [313, 311, 23476] C3 x C21 115) [5869, 622, 2817] C3 x C21
65) [349, 458, 17541] C3 x C21 81) [1949, 229, 8725] C3 x C21
66) [353, 1147, 318224] C3 x C21 134) [19889, 2294, 42713] C3 x C21
67) [397, 410, 40437] C3 x C21 ---) [4493, 205, 397] C3 x C3 x C21
68) [421, 1502, 503377] C3 x C21 ---) [10273, 751, 15156] C3 x C3 x C63
69) [617, 287, 19204] C3 x C21 110) [4801, 574, 5553] C3 x C21
70) [733, 114, 317] C3 x C21 ---) [317, 57, 733] C21
71) [761, 886, 1433] C3 x C21 ---) [1433, 443, 48704] C21
72) [953, 2791, 1861412] C3 x C21 124) [9497, 1675, 15248] C3 x C21
73) [1013, 1789, 799877] C3 x C21 109) [4733, 1381, 49637] C3 x C21
74) [1049, 219, 11728] C3 x C21 ---) [733, 438, 1049] C3 x C3 x C21
75) [1117, 733, 127341] C3 x C21 128) [14149, 1466, 27925] C3 x C21
76) [1213, 765, 109613] C3 x C21 86) [2237, 1530, 146773] C3 x C21
77) [1229, 49, 293] C3 x C21 ---) [293, 98, 1229] C21
78) [1229, 242, 9725] C3 x C21 ---) [389, 121, 1229] C21
79) [1229, 41, 113] C3 x C21 ---) [113, 82, 1229] C21
80) [1777, 2606, 304641] C3 x C21 100) [3761, 1303, 348292] C3 x C21
81) [1949, 229, 8725] C3 x C21 65) [349, 458, 17541] C3 x C21
82) [2089, 418, 35325] C3 x C21 ---) [157, 209, 2089] C21
83) [2213, 173, 6929] C3 x C21 ---) [41, 323, 8852] C21
84) [2213, 145, 277] C3 x C21 ---) [277, 290, 19917] C21
85) [2221, 709, 111789] C3 x C21 127) [12421, 1418, 55525] C3 x C21
86) [2237, 1530, 146773] C3 x C21 76) [1213, 765, 109613] C3 x C21
87) [2557, 269, 12337] C3 x C21 ---) [73, 347, 10228] C21
88) [2557, 650, 13573] C3 x C21 ---) [277, 325, 23013] C21
89) [2713, 83, 1044] C3 x C21 ---) [29, 166, 2713] C21
90) [2729, 1502, 171025] C3 x C21 119) [6841, 751, 98244] C3 x C21
91) [2777, 123, 3088] C3 x C21 ---) [193, 246, 2777] C21
92) [2777, 755, 86272] C3 x C21 ---) [337, 867, 177728] C21
93) [2857, 411, 7232] C3 x C21 ---) [113, 515, 45712] C21
94) [2857, 671, 106132] C3 x C21 ---) [157, 385, 25713] C21
95) [3041, 1878, 103225] C3 x C21 103) [4129, 939, 194624] C3 x C21
96) [3217, 1419, 213056] C3 x C21 99) [3329, 2838, 1161337] C3 x C21
97) [3229, 258, 3725] C3 x C21 ---) [149, 129, 3229] C21
98) [3229, 81, 833] C3 x C21 ---) [17, 162, 3229] C21
99) [3329, 2838, 1161337] C3 x C21 96) [3217, 1419, 213056] C3 x C21
100) [3761, 1303, 348292] C3 x C21 80) [1777, 2606, 304641] C3 x C21
101) [3877, 313, 261] C3 x C21 ---) [29, 217, 3877] C21
102) [4001, 199, 8900] C3 x C21 ---) [89, 398, 4001] C21
103) [4129, 939, 194624] C3 x C21 95) [3041, 1878, 103225] C3 x C21
104) [4481, 159, 5200] C3 x C21 ---) [13, 189, 4481] C21
105) [4481, 87, 772] C3 x C21 ---) [193, 174, 4481] C21
106) [4649, 1135, 125636] C3 x C21 ---) [641, 1315, 297536] C21
107) [4649, 343, 356] C3 x C21 ---) [89, 686, 116225] C21
108) [4729, 1075, 230976] C3 x C21 ---) [401, 891, 75664] C105
109) [4733, 1381, 49637] C3 x C21 73) [1013, 1789, 799877] C3 x C21
110) [4801, 574, 5553] C3 x C21 69) [617, 287, 19204] C3 x C21
111) [5261, 269, 6253] C3 x C21 ---) [37, 461, 47349] C21
112) [5281, 103, 1332] C3 x C21 ---) [37, 206, 5281] C21
113) [5281, 619, 62784] C3 x C21 ---) [109, 721, 47529] C21
114) [5297, 95, 932] C3 x C21 ---) [233, 190, 5297] C21
115) [5869, 622, 2817] C3 x C21 64) [313, 311, 23476] C3 x C21
116) [6133, 265, 3757] C3 x C21 ---) [13, 157, 6133] C21
117) [6373, 125, 2313] C3 x C21 ---) [257, 250, 6373] C3 x C3 x C21
118) [6637, 245, 73] C3 x C21 ---) [73, 490, 59733] C21
119) [6841, 751, 98244] C3 x C21 90) [2729, 1502, 171025] C3 x C21
120) [6917, 410, 14357] C3 x C21 63) [293, 205, 6917] C3 x C21
121) [9173, 741, 134977] C3 x C21 43) [73, 555, 36692] C3 x C21
122) [9281, 410, 4901] C3 x C21 ---) [29, 205, 9281] C21
123) [9397, 894, 49457] C3 x C21 46) [137, 447, 37588] C3 x C21
124) [9497, 1675, 15248] C3 x C21 72) [953, 2791, 1861412] C3 x C21
125) [10457, 123, 1168] C3 x C21 ---) [73, 246, 10457] C21
126) [11057, 547, 5696] C3 x C21 ---) [89, 1094, 276425] C21
127) [12421, 1418, 55525] C3 x C21 85) [2221, 709, 111789] C3 x C21
128) [14149, 1466, 27925] C3 x C21 75) [1117, 733, 127341] C3 x C21
129) [14197, 349, 26901] C3 x C21 ---) [61, 698, 14197] C21
130) [14197, 141, 1421] C3 x C21 ---) [29, 282, 14197] C21
131) [16529, 731, 96400] C3 x C21 56) [241, 1462, 148761] C3 x C21
132) [17581, 241, 10125] C3 x C21 ---) [5, 273, 17581] C21
133) [18257, 143, 548] C3 x C21 ---) [137, 286, 18257] C21
134) [19889, 2294, 42713] C3 x C21 66) [353, 1147, 318224] C3 x C21
135) [20233, 1131, 71936] C3 x C21 61) [281, 2262, 991417] C3 x C21
136) [20693, 189, 3757] C3 x C21 ---) [13, 378, 20693] C21
137) [23993, 155, 8] C3 x C21 ---) [8, 310, 23993] C21
138) [24281, 251, 9680] C3 x C21 ---) [5, 313, 24281] C21
139) [24317, 289, 14801] C3 x C21 39) [41, 578, 24317] C3 x C21
140) [25409, 247, 8900] C3 x C21 ---) [89, 494, 25409] C21
141) [25469, 313, 18125] C3 x C21 ---) [29, 626, 25469] C21
142) [28433, 1655, 336452] C3 x C21 54) [233, 2003, 454928] C3 x C21
143) [29573, 629, 91517] C3 x C21 48) [173, 1258, 29573] C3 x C21
144) [30937, 906, 81461] C3 x C21 34) [29, 453, 30937] C3 x C21
145) [31069, 706, 333] C3 x C21 ---) [37, 353, 31069] C21
146) [31249, 2687, 47236] C3 x C21 55) [241, 1475, 499984] C3 x C21
147) [35401, 195, 656] C3 x C21 ---) [41, 390, 35401] C21
148) [36469, 333, 18605] C3 x C21 ---) [5, 389, 36469] C21
149) [38453, 269, 8477] C3 x C21 49) [173, 538, 38453] C3 x C21
150) [41189, 818, 2525] C3 x C21 44) [101, 409, 41189] C3 x C21
151) [41549, 857, 173225] C3 x C21 40) [41, 1255, 166196] C3 x C21
152) [43913, 874, 15317] C3 x C21 41) [53, 437, 43913] C3 x C21
153) [47809, 1774, 21825] C3 x C21 ---) [97, 887, 191236] C21
154) [49481, 227, 512] C3 x C21 ---) [8, 454, 49481] C21
155) [50929, 279, 6728] C3 x C21 24) [8, 558, 50929] C3 x C21
156) [54409, 297, 8450] C3 x C21 ---) [8, 594, 54409] C21
157) [55721, 755, 128576] C3 x C21 ---) [41, 1510, 55721] C21
158) [60037, 373, 19773] C3 x C21 ---) [13, 746, 60037] C21
159) [62233, 315, 9248] C3 x C21 ---) [8, 630, 62233] C21
160) [62549, 493, 45125] C3 x C21 ---) [5, 529, 62549] C21
161) [63589, 533, 55125] C3 x C21 ---) [5, 549, 63589] C21
162) [63617, 1306, 171941] C3 x C21 33) [29, 653, 63617] C3 x C21
163) [68737, 317, 7938] C3 x C21 20) [8, 634, 68737] C3 x C21
164) [69821, 361, 15125] C3 x C21 ---) [5, 533, 69821] C21
165) [69833, 891, 181012] C3 x C21 29) [13, 597, 69833] C3 x C21
166) [71249, 343, 11600] C3 x C21 35) [29, 686, 71249] C3 x C21
167) [75941, 405, 22021] C3 x C21 42) [61, 810, 75941] C3 x C21
168) [78041, 283, 512] C3 x C21 ---) [8, 566, 78041] C21
169) [80629, 857, 2197] C3 x C21 ---) [13, 629, 80629] C21
170) [87149, 593, 66125] C3 x C21 ---) [5, 629, 87149] C21
171) [89069, 337, 6125] C3 x C21 ---) [5, 661, 89069] C21
172) [101489, 341, 3698] C3 x C21 27) [8, 682, 101489] C3 x C21
173) [104549, 677, 88445] C3 x C21 ---) [5, 701, 104549] C21
174) [117721, 379, 6480] C3 x C21 17) [5, 758, 117721] C3 x C21
175) [138041, 395, 4496] C3 x C21 62) [281, 790, 138041] C3 x C21
176) [142949, 437, 12005] C3 x C21 ---) [5, 821, 142949] C21
177) [147629, 593, 51005] C3 x C21 ---) [5, 769, 147629] C21
178) [164449, 687, 76880] C3 x C21 1) [5, 821, 164449] C3 x C21
179) [168409, 627, 56180] C3 x C21 5) [5, 821, 168409] C3 x C21
180) [202889, 667, 60500] C3 x C21 9) [5, 901, 202889] C3 x C21
181) [229981, 601, 32805] C3 x C21 11) [5, 993, 229981] C3 x C21
182) [245129, 547, 13520] C3 x C21 4) [5, 1094, 245129] C3 x C21
183) [256337, 2771, 317504] C3 x C21 38) [41, 2039, 1025348] C3 x C21
184) [344209, 727, 46080] C3 x C21 16) [5, 1221, 344209] C3 x C21
185) [368021, 1229, 285605] C3 x C21 15) [5, 1297, 368021] C3 x C21
186) [369913, 609, 242] C3 x C21 22) [8, 1218, 369913] C3 x C21
187) [378137, 635, 6272] C3 x C21 21) [8, 1270, 378137] C3 x C21
188) [409729, 1343, 348480] C3 x C21 3) [5, 1389, 409729] C3 x C21
189) [430649, 907, 98000] C3 x C21 14) [5, 1321, 430649] C3 x C21
190) [485729, 3851, 671744] C3 x C21 37) [41, 2815, 1942916] C3 x C21
191) [497977, 993, 122018] C3 x C21 23) [8, 1986, 497977] C3 x C21
192) [514357, 733, 5733] C3 x C21 28) [13, 1466, 514357] C3 x C21
193) [516421, 757, 14157] C3 x C21 32) [13, 1514, 516421] C3 x C21
194) [529181, 1049, 142805] C3 x C21 2) [5, 1457, 529181] C3 x C21
195) [564701, 809, 22445] C3 x C21 6) [5, 1618, 564701] C3 x C21
196) [672349, 873, 22445] C3 x C21 10) [5, 1746, 672349] C3 x C21
197) [848297, 1075, 76832] C3 x C21 26) [8, 2150, 848297] C3 x C21
198) [1082189, 1537, 320045] C3 x C21 7) [5, 2081, 1082189] C3 x C21
199) [1252469, 1517, 262205] C3 x C21 12) [5, 2261, 1252469] C3 x C21
200) [1268537, 1217, 53138] C3 x C21 18) [8, 2434, 1268537] C3 x C21