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 C130 non-normal (D4) quartic CM field invariants: 204 fields

K Quartic invariants Cl(OK) Igusa invariants Kr Reflex invariants Cl(OKr) Igusa invariants
1) [5, 1702, 683701] C5 x C130 184) [683701, 851, 10125] C5 x C130
2) [5, 10030, 23491345] C5 x C130 ---) [23491345, 5015, 414720] C5 x C520
3) [5, 11006, 29771009] C5 x C130 ---) [29771009, 5503, 128000] C5 x C390
4) [5, 5590, 7578745] C5 x C130 ---) [7578745, 2795, 58320] C5 x C520
5) [8, 5390, 7262897] C5 x C130 ---) [7262897, 2695, 32] C5 x C5 x C650
6) [21, 3718, 2476105] C5 x C130 ---) [2476105, 1859, 244944] C5 x C1560
7) [41, 7942, 12368137] C5 x C130 204) [12368137, 3971, 850176] C5 x C130
8) [61, 1566, 314189] C5 x C130 ---) [314189, 783, 74725] C5 x C5 x C130
9) [61, 2246, 1206229] C5 x C130 ---) [1206229, 1123, 13725] C5 x C5 x C130
10) [172, 1284, 246872] C5 x C130 170) [246872, 642, 41323] C5 x C130
11) [197, 1270, 374857] C5 x C130 175) [374857, 635, 7092] C5 x C130
12) [248, 4124, 560612] C5 x C130 ---) [140153, 2062, 922808] C5 x C520
13) [268, 816, 18461] C5 x C130 106) [18461, 1632, 592012] C5 x C130
14) [268, 2366, 434689] C5 x C130 177) [434689, 1183, 241200] C5 x C130
15) [281, 1555, 166076] C5 x C130 159) [166076, 3110, 1753721] C5 x C130
16) [349, 2610, 1634621] C5 x C130 ---) [1634621, 1305, 17101] C5 x C4160
17) [349, 455, 20259] C5 x C130 ---) [9004, 910, 125989] C5 x C910
18) [376, 1858, 664137] C5 x C130 ---) [73793, 929, 49726] C5 x C260
19) [401, 258, 15037] C5 x C130 ---) [15037, 129, 401] C130
20) [401, 1591, 627908] C5 x C130 ---) [156977, 3182, 19649] C2 x C390
21) [401, 133, 1916] C5 x C130 ---) [1916, 266, 10025] C130
22) [401, 1070, 228481] C5 x C130 ---) [228481, 535, 14436] C130
23) [401, 934, 115433] C5 x C130 ---) [115433, 467, 25664] C2 x C130
24) [412, 4022, 1908313] C5 x C130 197) [1908313, 2011, 533952] C5 x C130
25) [428, 1152, 208084] C5 x C130 135) [52021, 576, 30923] C5 x C130
26) [437, 1038, 241393] C5 x C130 168) [241393, 519, 6992] C5 x C130
27) [556, 2396, 792468] C5 x C130 112) [22013, 1198, 160684] C5 x C130
28) [677, 1461, 484717] C5 x C130 179) [484717, 2922, 195653] C5 x C130
29) [817, 379, 11196] C5 x C130 ---) [1244, 758, 98857] C130
30) [817, 1138, 163629] C5 x C130 ---) [18181, 569, 40033] C130
31) [817, 887, 180148] C5 x C130 ---) [45037, 1774, 66177] C1040
32) [817, 1367, 450628] C5 x C130 ---) [112657, 2734, 66177] C130
33) [844, 5718, 7687737] C5 x C130 188) [854193, 2859, 121536] C5 x C130
34) [1093, 1662, 620609] C5 x C130 ---) [5129, 831, 17488] C130
35) [1093, 802, 107244] C5 x C130 ---) [1324, 1024, 245925] C130
36) [1093, 845, 178233] C5 x C130 ---) [1473, 1131, 157392] C130
37) [1093, 578, 73684] C5 x C130 ---) [109, 458, 4372] C130
38) [1093, 1285, 412533] C5 x C130 ---) [5093, 2241, 184717] C130
39) [1117, 4150, 3161817] C5 x C130 173) [351313, 2075, 285952] C5 x C130
40) [1177, 2609, 1454256] C5 x C130 ---) [40396, 5218, 989857] C5 x C390
41) [1349, 1245, 370981] C5 x C130 ---) [370981, 2490, 66101] C5 x C260
42) [1429, 121, 445] C5 x C130 ---) [445, 242, 12861] C520
43) [1432, 2354, 525771] C5 x C130 114) [25964, 2706, 1512550] C5 x C130
44) [1468, 992, 244548] C5 x C130 79) [6793, 496, 367] C5 x C130
45) [1516, 5146, 16633] C5 x C130 102) [16633, 2573, 1650924] C5 x C130
46) [1641, 818, 3181] C5 x C130 61) [3181, 409, 41025] C5 x C130
47) [1641, 1191, 55548] C5 x C130 ---) [6172, 2382, 1196289] C130
48) [1641, 503, 52996] C5 x C130 ---) [13249, 1006, 41025] C130
49) [1641, 185, 8146] C5 x C130 ---) [32584, 370, 1641] C520
50) [1641, 461, 19900] C5 x C130 ---) [796, 922, 132921] C130
51) [1756, 810, 157001] C5 x C130 ---) [929, 405, 1756] C130
52) [1756, 944, 10308] C5 x C130 ---) [2577, 472, 53119] C130
53) [1756, 1152, 119300] C5 x C130 ---) [1193, 576, 53119] C130
54) [1897, 383, 32404] C5 x C130 ---) [8101, 766, 17073] C13 x C130
55) [1996, 570, 9369] C5 x C130 ---) [1041, 285, 17964] C130
56) [2033, 1511, 82352] C5 x C130 110) [20588, 3022, 1953713] C5 x C130
57) [2081, 914, 40288] C5 x C130 ---) [10072, 1828, 674244] C130
58) [2481, 565, 74224] C5 x C130 107) [18556, 1130, 22329] C5 x C130
59) [2841, 136, 1783] C5 x C130 80) [7132, 272, 11364] C5 x C130
60) [3169, 5672, 8014375] C5 x C130 133) [51292, 11344, 114084] C5 x C130
61) [3181, 409, 41025] C5 x C130 46) [1641, 818, 3181] C5 x C130
62) [3181, 197, 2545] C5 x C130 ---) [2545, 394, 28629] C520
63) [3253, 445, 9657] C5 x C130 ---) [1073, 890, 159397] C2 x C130
64) [3253, 2585, 986613] C5 x C130 ---) [2733, 2173, 1174333] C130
65) [3637, 3513, 1556843] C5 x C130 111) [21548, 7026, 6113797] C5 x C130
66) [3928, 210, 10043] C5 x C130 ---) [332, 420, 3928] C130
67) [4253, 1598, 213101] C5 x C130 68) [4349, 799, 106325] C5 x C130
68) [4349, 799, 106325] C5 x C130 67) [4253, 1598, 213101] C5 x C130
69) [4353, 383, 35584] C5 x C130 ---) [556, 766, 4353] C130
70) [4441, 475, 2004] C5 x C130 ---) [501, 950, 217609] C130
71) [4504, 500, 57996] C5 x C130 ---) [716, 250, 1126] C130
72) [4504, 1884, 4580] C5 x C130 ---) [1145, 942, 220696] C520
73) [4504, 274, 14265] C5 x C130 ---) [1585, 137, 1126] C260
74) [4801, 7327, 12786300] C5 x C130 139) [56828, 14654, 2539729] C5 x C130
75) [5209, 7785, 242096] C5 x C130 ---) [60524, 15570, 59637841] C5 x C5 x C390
76) [5944, 750, 45521] C5 x C130 ---) [929, 375, 23776] C130
77) [6113, 319, 23912] C5 x C130 ---) [488, 638, 6113] C2 x C130
78) [6481, 111, 1460] C5 x C130 ---) [365, 222, 6481] C2 x C130
79) [6793, 496, 367] C5 x C130 44) [1468, 992, 244548] C5 x C130
80) [7132, 272, 11364] C5 x C130 59) [2841, 136, 1783] C5 x C130
81) [7817, 399, 22212] C5 x C130 ---) [617, 798, 70353] C130
82) [8108, 1384, 276164] C5 x C130 ---) [1409, 692, 50675] C130
83) [8108, 1138, 321734] C5 x C130 ---) [536, 598, 50675] C130
84) [8501, 1753, 1037] C5 x C130 ---) [1037, 2677, 1436669] C2 x C130
85) [8501, 607, 89987] C5 x C130 ---) [428, 1214, 8501] C130
86) [8501, 95, 131] C5 x C130 ---) [524, 190, 8501] C130
87) [9596, 3616, 3182500] C5 x C130 ---) [1273, 1808, 21591] C130
88) [9829, 1477, 542925] C5 x C130 ---) [2413, 2954, 9829] C130
89) [10613, 626, 55517] C5 x C130 ---) [1133, 313, 10613] C130
90) [10909, 218, 972] C5 x C130 ---) [12, 328, 10909] C130
91) [10909, 553, 73725] C5 x C130 ---) [2949, 1106, 10909] C130
92) [11273, 163, 3824] C5 x C130 ---) [956, 326, 11273] C130
93) [11409, 1397, 5872] C5 x C130 ---) [1468, 2794, 1928121] C130
94) [12041, 1345, 208426] C5 x C130 ---) [1576, 2690, 975321] C2 x C130
95) [12101, 446, 1325] C5 x C130 ---) [53, 223, 12101] C130
96) [12101, 248, 3275] C5 x C130 ---) [524, 496, 48404] C130
97) [12301, 222, 20] C5 x C130 ---) [5, 444, 49204] C130
98) [12301, 754, 92925] C5 x C130 ---) [413, 377, 12301] C130
99) [12952, 228, 44] C5 x C130 ---) [44, 114, 3238] C130
100) [15121, 1882, 824997] C5 x C130 ---) [237, 941, 15121] C130
101) [16313, 171, 3232] C5 x C130 ---) [808, 342, 16313] C260
102) [16633, 2573, 1650924] C5 x C130 45) [1516, 5146, 16633] C5 x C130
103) [17033, 1687, 605036] C5 x C130 ---) [1676, 3374, 425825] C130
104) [17084, 1312, 3236] C5 x C130 ---) [809, 656, 106775] C130
105) [18353, 397, 34814] C5 x C130 ---) [824, 794, 18353] C130
106) [18461, 1632, 592012] C5 x C130 13) [268, 816, 18461] C5 x C130
107) [18556, 1130, 22329] C5 x C130 58) [2481, 565, 74224] C5 x C130
108) [20089, 1869, 265598] C5 x C130 ---) [632, 3738, 2430769] C130
109) [20428, 512, 19573] C5 x C130 ---) [37, 818, 20428] C130
110) [20588, 3022, 1953713] C5 x C130 56) [2033, 1511, 82352] C5 x C130
111) [21548, 7026, 6113797] C5 x C130 65) [3637, 3513, 1556843] C5 x C130
112) [22013, 1198, 160684] C5 x C130 27) [556, 2396, 792468] C5 x C130
113) [22844, 1664, 486628] C5 x C130 ---) [337, 832, 51399] C130
114) [25964, 2706, 1512550] C5 x C130 43) [1432, 2354, 525771] C5 x C130
115) [26252, 592, 61364] C5 x C130 ---) [29, 296, 6563] C130
116) [26252, 2392, 1194148] C5 x C130 ---) [1033, 1196, 59067] C130
117) [27749, 293, 14525] C5 x C130 ---) [581, 586, 27749] C130
118) [30341, 871, 29] C5 x C130 ---) [29, 655, 30341] C130
119) [30893, 1255, 15317] C5 x C130 ---) [53, 815, 30893] C130
120) [30949, 653, 98865] C5 x C130 ---) [65, 1306, 30949] C2 x C130
121) [33029, 277, 10925] C5 x C130 ---) [437, 554, 33029] C130
122) [34309, 397, 30825] C5 x C130 ---) [137, 794, 34309] C130
123) [34588, 1024, 227556] C5 x C130 ---) [129, 512, 8647] C5 x C10
124) [34828, 560, 37] C5 x C130 ---) [37, 1120, 313452] C130
125) [34828, 546, 39701] C5 x C130 ---) [29, 273, 8707] C130
126) [34828, 1128, 4644] C5 x C130 ---) [129, 564, 78363] C130
127) [37484, 1024, 27869] C5 x C130 ---) [29, 994, 37484] C130
128) [37781, 225, 3211] C5 x C130 ---) [76, 450, 37781] C130
129) [42268, 1408, 453348] C5 x C130 ---) [257, 704, 10567] C390
130) [42956, 432, 3700] C5 x C130 ---) [37, 216, 10739] C130
131) [49081, 1587, 28400] C5 x C130 ---) [284, 3174, 2404969] C130
132) [50476, 454, 1053] C5 x C130 ---) [13, 227, 12619] C5 x C10
133) [51292, 11344, 114084] C5 x C130 60) [3169, 5672, 8014375] C5 x C130
134) [51953, 458, 488] C5 x C130 ---) [488, 916, 207812] C260
135) [52021, 576, 30923] C5 x C130 25) [428, 1152, 208084] C5 x C130
136) [52684, 7784, 3293764] C5 x C130 ---) [2281, 3892, 2963475] C130
137) [55576, 350, 16731] C5 x C130 ---) [44, 700, 55576] C130
138) [55961, 2062, 167585] C5 x C130 ---) [1385, 1031, 223844] C260
139) [56828, 14654, 2539729] C5 x C130 74) [4801, 7327, 12786300] C5 x C130
140) [59149, 682, 57132] C5 x C130 ---) [12, 536, 59149] C130
141) [62873, 1763, 6848] C5 x C130 ---) [428, 3526, 3080777] C130
142) [66829, 1410, 229709] C5 x C130 ---) [29, 705, 66829] C130
143) [71132, 1198, 74273] C5 x C130 ---) [257, 599, 71132] C390
144) [73756, 278, 882] C5 x C130 ---) [8, 278, 18439] C130
145) [76173, 1178, 42229] C5 x C130 ---) [349, 589, 76173] C130
146) [76597, 305, 4107] C5 x C130 ---) [12, 610, 76597] C130
147) [84716, 592, 2900] C5 x C130 ---) [29, 296, 21179] C130
148) [85628, 1174, 2057] C5 x C130 ---) [17, 587, 85628] C130
149) [93337, 347, 6768] C5 x C130 ---) [188, 694, 93337] C130
150) [99633, 848, 80143] C5 x C130 ---) [28, 1696, 398532] C130
151) [120829, 349, 243] C5 x C130 ---) [12, 698, 120829] C130
152) [129229, 1258, 266412] C5 x C130 ---) [12, 728, 129229] C130
153) [133717, 367, 243] C5 x C130 ---) [12, 734, 133717] C130
154) [137993, 515, 31808] C5 x C130 ---) [497, 1030, 137993] C130
155) [142257, 2147, 263296] C5 x C130 ---) [136, 4294, 3556425] C260
156) [145592, 914, 63257] C5 x C130 ---) [17, 457, 36398] C130
157) [161921, 872, 28175] C5 x C130 ---) [92, 1744, 647684] C130
158) [165777, 1371, 96912] C5 x C130 ---) [673, 2742, 1491993] C130
159) [166076, 3110, 1753721] C5 x C130 15) [281, 1555, 166076] C5 x C130
160) [171809, 5539, 411200] C5 x C130 ---) [257, 4163, 2748944] C390
161) [172633, 421, 1152] C5 x C130 ---) [8, 842, 172633] C130
162) [181121, 511, 20000] C5 x C130 ---) [8, 1022, 181121] C130
163) [183452, 518, 21218] C5 x C130 ---) [8, 518, 45863] C130
164) [194716, 992, 51300] C5 x C130 ---) [57, 496, 48679] C130
165) [222424, 472, 90] C5 x C130 ---) [40, 944, 222424] C260
166) [222881, 1427, 7600] C5 x C130 ---) [76, 2854, 2005929] C130
167) [238321, 583, 25392] C5 x C130 ---) [12, 1166, 238321] C130
168) [241393, 519, 6992] C5 x C130 26) [437, 1038, 241393] C5 x C130
169) [244364, 994, 2645] C5 x C130 ---) [5, 497, 61091] C130
170) [246872, 642, 41323] C5 x C130 10) [172, 1284, 246872] C5 x C130
171) [306377, 573, 5488] C5 x C130 ---) [28, 1146, 306377] C130
172) [330329, 623, 14450] C5 x C130 ---) [8, 1246, 330329] C130
173) [351313, 2075, 285952] C5 x C130 39) [1117, 4150, 3161817] C5 x C130
174) [355129, 1579, 534528] C5 x C130 ---) [232, 3158, 355129] C260
175) [374857, 635, 7092] C5 x C130 11) [197, 1270, 374857] C5 x C130
176) [409817, 1243, 283808] C5 x C130 ---) [1448, 2486, 409817] C10 x C130
177) [434689, 1183, 241200] C5 x C130 14) [268, 2366, 434689] C5 x C130
178) [441353, 803, 50864] C5 x C130 ---) [44, 1606, 441353] C130
179) [484717, 2922, 195653] C5 x C130 28) [677, 1461, 484717] C5 x C130
180) [513433, 2255, 116032] C5 x C130 ---) [37, 4510, 4620897] C130
181) [546673, 761, 8112] C5 x C130 ---) [12, 1522, 546673] C130
182) [548677, 745, 1587] C5 x C130 ---) [12, 1490, 548677] C130
183) [629313, 801, 3072] C5 x C130 ---) [12, 1602, 629313] C130
184) [683701, 851, 10125] C5 x C130 1) [5, 1702, 683701] C5 x C130
185) [689609, 1283, 239120] C5 x C130 ---) [305, 2566, 689609] C260
186) [753609, 1019, 71188] C5 x C130 ---) [13, 2038, 753609] C130
187) [835657, 915, 392] C5 x C130 ---) [8, 1830, 835657] C130
188) [854193, 2859, 121536] C5 x C130 33) [844, 5718, 7687737] C5 x C130
189) [862033, 1001, 34992] C5 x C130 ---) [12, 2002, 862033] C130
190) [1028569, 1051, 19008] C5 x C130 ---) [33, 2102, 1028569] C130
191) [1231761, 2222, 2560] C5 x C130 ---) [40, 4444, 4927044] C260
192) [1263481, 1291, 100800] C5 x C130 ---) [28, 2582, 1263481] C130
193) [1348377, 1275, 69312] C5 x C130 ---) [12, 2550, 1348377] C130
194) [1360113, 1209, 25392] C5 x C130 ---) [12, 2418, 1360113] C130
195) [1390969, 1963, 615600] C5 x C130 ---) [76, 3926, 1390969] C130
196) [1551049, 2083, 696960] C5 x C130 ---) [40, 4166, 1551049] C2 x C130
197) [1908313, 2011, 533952] C5 x C130 24) [412, 4022, 1908313] C5 x C130
198) [2125993, 2419, 931392] C5 x C130 ---) [33, 4838, 2125993] C130
199) [2360089, 2107, 519840] C5 x C130 ---) [40, 4214, 2360089] C2 x C130
200) [2435593, 1795, 196608] C5 x C130 ---) [12, 3590, 2435593] C130
201) [2479513, 2491, 931392] C5 x C130 ---) [33, 4982, 2479513] C130
202) [2550993, 1599, 1452] C5 x C130 ---) [12, 3198, 2550993] C130
203) [2876953, 1915, 197568] C5 x C130 ---) [28, 3830, 2876953] C130
204) [12368137, 3971, 850176] C5 x C130 7) [41, 7942, 12368137] C5 x C130