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 C15 non-normal (D4) quartic CM field invariants: 161 fields

K Quartic invariants Cl(OK) Igusa invariants Kr Reflex invariants Cl(OKr) Igusa invariants
1) [5, 757, 114761] C3 x C15 145) [114761, 379, 7220] C3 x C15
2) [5, 1266, 390109] C3 x C15 157) [390109, 633, 2645] C3 x C15
3) [5, 1097, 257141] C3 x C15 ---) [257141, 589, 22445] C3 x C15 x C15
4) [5, 922, 188021] C3 x C15 148) [188021, 461, 6125] C3 x C15
5) [5, 1306, 374389] C3 x C15 156) [374389, 653, 13005] C3 x C15
6) [5, 673, 108881] C3 x C15 143) [108881, 431, 19220] C3 x C15
7) [5, 1189, 345229] C3 x C15 155) [345229, 993, 160205] C3 x C15
8) [5, 989, 231269] C3 x C15 150) [231269, 613, 36125] C3 x C15
9) [5, 1349, 429389] C3 x C15 158) [429389, 833, 66125] C3 x C15
10) [5, 809, 157669] C3 x C15 146) [157669, 693, 80645] C3 x C15
11) [5, 578, 81901] C3 x C15 142) [81901, 289, 405] C3 x C15
12) [5, 1594, 587189] C3 x C15 160) [587189, 797, 12005] C3 x C15
13) [8, 838, 172969] C3 x C15 147) [172969, 419, 648] C3 x C15
14) [8, 2150, 754217] C3 x C15 161) [754217, 1075, 100352] C3 x C15
15) [8, 314, 15937] C3 x C15 108) [15937, 157, 2178] C3 x C15
16) [8, 1218, 188473] C3 x C15 149) [188473, 609, 45602] C3 x C15
17) [8, 1138, 265961] C3 x C15 151) [265961, 569, 14450] C3 x C15
18) [8, 1330, 304937] C3 x C15 154) [304937, 665, 34322] C3 x C15
19) [8, 490, 57713] C3 x C15 ---) [57713, 245, 578] C3 x C165
20) [13, 345, 26633] C3 x C15 120) [26633, 503, 3328] C3 x C15
21) [17, 1230, 299617] C3 x C15 153) [299617, 615, 19652] C3 x C15
22) [17, 734, 112657] C3 x C15 144) [112657, 367, 5508] C3 x C15
23) [17, 1654, 500057] C3 x C15 159) [500057, 827, 45968] C3 x C15
24) [17, 1150, 284657] C3 x C15 152) [284657, 575, 11492] C3 x C15
25) [17, 922, 49253] C3 x C15 139) [49253, 461, 40817] C3 x C15
26) [29, 505, 16189] C3 x C15 109) [16189, 637, 261] C3 x C15
27) [29, 750, 49681] C3 x C15 ---) [49681, 375, 22736] C3 x C3 x C15
28) [41, 306, 19309] C3 x C15 113) [19309, 153, 1025] C3 x C15
29) [41, 839, 118324] C3 x C15 125) [29581, 909, 21689] C3 x C15
30) [41, 1431, 511684] C3 x C15 ---) [127921, 1891, 94464] C15 x C15
31) [53, 1021, 46901] C3 x C15 138) [46901, 1541, 19133] C3 x C15
32) [53, 1341, 43789] C3 x C15 135) [43789, 1481, 11925] C3 x C15
33) [61, 1165, 213021] C3 x C15 118) [23669, 849, 32269] C3 x C15
34) [73, 1294, 277281] C3 x C15 126) [30809, 647, 35332] C3 x C15
35) [73, 946, 209421] C3 x C15 116) [23269, 473, 3577] C3 x C15
36) [89, 446, 36913] C3 x C15 133) [36913, 223, 3204] C3 x C15
37) [97, 442, 39141] C3 x C15 84) [4349, 221, 2425] C3 x C15
38) [97, 1323, 353168] C3 x C15 115) [22073, 1035, 262288] C3 x C15
39) [109, 909, 9689] C3 x C15 99) [9689, 655, 85456] C3 x C15
40) [113, 1166, 34337] C3 x C15 131) [34337, 583, 76388] C3 x C15
41) [137, 406, 32441] C3 x C15 128) [32441, 203, 2192] C3 x C15
42) [149, 473, 10301] C3 x C15 ---) [10301, 946, 182525] C3 x C3 x C15
43) [157, 781, 98757] C3 x C15 103) [10973, 1105, 83053] C3 x C15
44) [173, 162, 5869] C3 x C15 92) [5869, 81, 173] C3 x C15
45) [173, 789, 5077] C3 x C15 87) [5077, 557, 76293] C3 x C15
46) [229, 409, 34893] C3 x C15 82) [3877, 818, 27709] C3 x C15
47) [229, 306, 509] C3 x C15 ---) [509, 153, 5725] C15
48) [229, 965, 5581] C3 x C15 ---) [5581, 1121, 229] C15
49) [229, 893, 194725] C3 x C15 ---) [7789, 1097, 143125] C15
50) [257, 215, 6352] C3 x C15 ---) [397, 261, 257] C15
51) [257, 142, 929] C3 x C15 ---) [929, 71, 1028] C15
52) [257, 151, 5636] C3 x C15 ---) [1409, 302, 257] C15
53) [257, 518, 1289] C3 x C15 ---) [1289, 259, 16448] C15
54) [269, 997, 224225] C3 x C15 97) [8969, 1519, 520784] C3 x C15
55) [269, 785, 5501] C3 x C15 91) [5501, 1021, 226229] C3 x C15
56) [281, 911, 121424] C3 x C15 94) [7589, 1205, 270041] C3 x C15
57) [313, 950, 45337] C3 x C15 136) [45337, 475, 45072] C3 x C15
58) [317, 97, 2273] C3 x C15 75) [2273, 194, 317] C3 x C15
59) [337, 927, 12548] C3 x C15 ---) [3137, 611, 86272] C3 x C3 x C45
60) [389, 1753, 429725] C3 x C15 111) [17189, 2041, 933989] C3 x C15
61) [457, 1307, 417808] C3 x C15 ---) [26113, 2614, 37017] C3 x C3 x C15
62) [653, 718, 118433] C3 x C15 77) [2417, 359, 2612] C3 x C15
63) [761, 711, 57700] C3 x C15 ---) [577, 423, 3044] C105
64) [773, 230, 857] C3 x C15 66) [857, 115, 3092] C3 x C15
65) [809, 1038, 256417] C3 x C15 88) [5233, 519, 3236] C3 x C15
66) [857, 115, 3092] C3 x C15 64) [773, 230, 857] C3 x C15
67) [941, 138, 997] C3 x C15 68) [997, 69, 941] C3 x C15
68) [997, 69, 941] C3 x C15 67) [941, 138, 997] C3 x C15
69) [1049, 870, 122089] C3 x C15 ---) [1009, 435, 16784] C3 x C105
70) [1229, 310, 4361] C3 x C15 ---) [89, 155, 4916] C15
71) [1481, 1491, 448768] C3 x C15 73) [1753, 1011, 23696] C3 x C15
72) [1721, 1807, 227300] C3 x C15 76) [2273, 1123, 110144] C3 x C15
73) [1753, 1011, 23696] C3 x C15 71) [1481, 1491, 448768] C3 x C15
74) [2089, 899, 84544] C3 x C15 ---) [1321, 1595, 133696] C15
75) [2273, 194, 317] C3 x C15 58) [317, 97, 2273] C3 x C15
76) [2273, 1123, 110144] C3 x C15 72) [1721, 1807, 227300] C3 x C15
77) [2417, 359, 2612] C3 x C15 62) [653, 718, 118433] C3 x C15
78) [2677, 165, 6137] C3 x C15 ---) [17, 207, 10708] C15
79) [2801, 1231, 221284] C3 x C15 ---) [1129, 1635, 44816] C3 x C3 x C45
80) [3049, 4339, 1486224] C3 x C15 100) [10321, 4295, 4402756] C3 x C15
81) [3529, 6491, 806464] C3 x C15 105) [12601, 3895, 1143396] C3 x C15
82) [3877, 818, 27709] C3 x C15 46) [229, 409, 34893] C3 x C15
83) [3877, 845, 99997] C3 x C15 ---) [277, 637, 34893] C15
84) [4349, 221, 2425] C3 x C15 37) [97, 442, 39141] C3 x C15
85) [4493, 354, 13357] C3 x C15 ---) [37, 177, 4493] C15
86) [4649, 659, 107408] C3 x C15 ---) [137, 619, 74384] C15
87) [5077, 557, 76293] C3 x C15 45) [173, 789, 5077] C3 x C15
88) [5233, 519, 3236] C3 x C15 65) [809, 1038, 256417] C3 x C15
89) [5261, 389, 4949] C3 x C15 ---) [101, 737, 131525] C15
90) [5261, 81, 325] C3 x C15 ---) [13, 162, 5261] C15
91) [5501, 1021, 226229] C3 x C15 55) [269, 785, 5501] C3 x C15
92) [5869, 81, 173] C3 x C15 44) [173, 162, 5869] C3 x C15
93) [6997, 317, 23373] C3 x C15 ---) [53, 585, 6997] C15
94) [7589, 1205, 270041] C3 x C15 56) [281, 911, 121424] C3 x C15
95) [8069, 309, 21853] C3 x C15 ---) [13, 201, 8069] C15
96) [8581, 101, 405] C3 x C15 ---) [5, 202, 8581] C15
97) [8969, 1519, 520784] C3 x C15 54) [269, 997, 224225] C3 x C15
98) [9281, 151, 3380] C3 x C15 ---) [5, 193, 9281] C15
99) [9689, 655, 85456] C3 x C15 39) [109, 909, 9689] C3 x C15
100) [10321, 4295, 4402756] C3 x C15 80) [3049, 4339, 1486224] C3 x C15
101) [10889, 131, 1568] C3 x C15 ---) [8, 262, 10889] C15
102) [10949, 337, 3757] C3 x C15 ---) [13, 213, 10949] C15
103) [10973, 1105, 83053] C3 x C15 43) [157, 781, 98757] C3 x C15
104) [12197, 165, 3757] C3 x C15 ---) [13, 330, 12197] C15
105) [12601, 3895, 1143396] C3 x C15 81) [3529, 6491, 806464] C3 x C15
106) [14389, 641, 12789] C3 x C15 ---) [29, 341, 14389] C15
107) [15661, 562, 16317] C3 x C15 ---) [37, 281, 15661] C15
108) [15937, 157, 2178] C3 x C15 15) [8, 314, 15937] C3 x C15
109) [16189, 637, 261] C3 x C15 26) [29, 505, 16189] C3 x C15
110) [16481, 199, 5780] C3 x C15 ---) [5, 257, 16481] C15
111) [17189, 2041, 933989] C3 x C15 60) [389, 1753, 429725] C3 x C15
112) [18269, 713, 122525] C3 x C15 ---) [29, 401, 18269] C15
113) [19309, 153, 1025] C3 x C15 28) [41, 306, 19309] C3 x C15
114) [20353, 151, 612] C3 x C15 ---) [17, 302, 20353] C15
115) [22073, 1035, 262288] C3 x C15 38) [97, 1323, 353168] C3 x C15
116) [23269, 473, 3577] C3 x C15 35) [73, 946, 209421] C3 x C15
117) [23609, 299, 16448] C3 x C15 ---) [257, 598, 23609] C3 x C3 x C15
118) [23669, 849, 32269] C3 x C15 33) [61, 1165, 213021] C3 x C15
119) [26489, 163, 20] C3 x C15 ---) [5, 326, 26489] C15
120) [26633, 503, 3328] C3 x C15 20) [13, 345, 26633] C3 x C15
121) [26893, 289, 14157] C3 x C15 ---) [13, 578, 26893] C15
122) [27617, 167, 68] C3 x C15 ---) [17, 334, 27617] C15
123) [28097, 247, 8228] C3 x C15 ---) [17, 494, 28097] C15
124) [28309, 173, 405] C3 x C15 ---) [5, 346, 28309] C15
125) [29581, 909, 21689] C3 x C15 29) [41, 839, 118324] C3 x C15
126) [30809, 647, 35332] C3 x C15 34) [73, 1294, 277281] C3 x C15
127) [30829, 177, 125] C3 x C15 ---) [5, 354, 30829] C15
128) [32441, 203, 2192] C3 x C15 41) [137, 406, 32441] C3 x C15
129) [33581, 241, 6125] C3 x C15 ---) [5, 373, 33581] C15
130) [33641, 275, 10496] C3 x C15 ---) [41, 550, 33641] C15
131) [34337, 583, 76388] C3 x C15 40) [113, 1166, 34337] C3 x C15
132) [35401, 201, 1250] C3 x C15 ---) [8, 402, 35401] C15
133) [36913, 223, 3204] C3 x C15 36) [89, 446, 36913] C3 x C15
134) [42709, 349, 19773] C3 x C15 ---) [13, 698, 42709] C15
135) [43789, 1481, 11925] C3 x C15 32) [53, 1341, 43789] C3 x C15
136) [45337, 475, 45072] C3 x C15 57) [313, 950, 45337] C3 x C15
137) [46589, 217, 125] C3 x C15 ---) [5, 434, 46589] C15
138) [46901, 1541, 19133] C3 x C15 31) [53, 1021, 46901] C3 x C15
139) [49253, 461, 40817] C3 x C15 25) [17, 922, 49253] C3 x C15
140) [57373, 917, 81133] C3 x C15 ---) [13, 485, 57373] C15
141) [63629, 257, 605] C3 x C15 ---) [5, 514, 63629] C15
142) [81901, 289, 405] C3 x C15 11) [5, 578, 81901] C3 x C15
143) [108881, 431, 19220] C3 x C15 6) [5, 673, 108881] C3 x C15
144) [112657, 367, 5508] C3 x C15 22) [17, 734, 112657] C3 x C15
145) [114761, 379, 7220] C3 x C15 1) [5, 757, 114761] C3 x C15
146) [157669, 693, 80645] C3 x C15 10) [5, 809, 157669] C3 x C15
147) [172969, 419, 648] C3 x C15 13) [8, 838, 172969] C3 x C15
148) [188021, 461, 6125] C3 x C15 4) [5, 922, 188021] C3 x C15
149) [188473, 609, 45602] C3 x C15 16) [8, 1218, 188473] C3 x C15
150) [231269, 613, 36125] C3 x C15 8) [5, 989, 231269] C3 x C15
151) [265961, 569, 14450] C3 x C15 17) [8, 1138, 265961] C3 x C15
152) [284657, 575, 11492] C3 x C15 24) [17, 1150, 284657] C3 x C15
153) [299617, 615, 19652] C3 x C15 21) [17, 1230, 299617] C3 x C15
154) [304937, 665, 34322] C3 x C15 18) [8, 1330, 304937] C3 x C15
155) [345229, 993, 160205] C3 x C15 7) [5, 1189, 345229] C3 x C15
156) [374389, 653, 13005] C3 x C15 5) [5, 1306, 374389] C3 x C15
157) [390109, 633, 2645] C3 x C15 2) [5, 1266, 390109] C3 x C15
158) [429389, 833, 66125] C3 x C15 9) [5, 1349, 429389] C3 x C15
159) [500057, 827, 45968] C3 x C15 23) [17, 1654, 500057] C3 x C15
160) [587189, 797, 12005] C3 x C15 12) [5, 1594, 587189] C3 x C15
161) [754217, 1075, 100352] C3 x C15 14) [8, 2150, 754217] C3 x C15