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 C195 non-normal (D4) quartic CM field invariants: 154 fields

K Quartic invariants Cl(OK) Igusa invariants Kr Reflex invariants Cl(OKr) Igusa invariants
1) [8, 10294, 26488409] C3 x C195 154) [26488409, 5147, 800] C3 x C195
2) [13, 6561, 10662149] C3 x C195 ---) [10662149, 10913, 5783557] C3 x C3 x C195
3) [13, 8349, 16107701] C3 x C195 ---) [16107701, 16681, 33321613] C3 x C3 x C1755
4) [13, 7958, 15802489] C3 x C195 153) [15802489, 3979, 7488] C3 x C195
5) [53, 3230, 1943393] C3 x C195 133) [1943393, 1615, 166208] C3 x C195
6) [113, 1690, 659333] C3 x C195 ---) [659333, 845, 13673] C15 x C195
7) [137, 5462, 3951161] C3 x C195 141) [3951161, 2731, 876800] C3 x C195
8) [229, 7517, 8227225] C3 x C195 ---) [329089, 5303, 366400] C195
9) [229, 3254, 2515225] C3 x C195 ---) [100609, 1627, 32976] C195
10) [229, 3054, 41729] C3 x C195 ---) [41729, 1527, 572500] C195
11) [229, 1098, 36677] C3 x C195 100) [36677, 549, 66181] C3 x C195
12) [229, 677, 101701] C3 x C195 ---) [101701, 1354, 51525] C195
13) [229, 318, 21617] C3 x C195 ---) [21617, 159, 916] C195
14) [229, 726, 40169] C3 x C195 ---) [40169, 363, 22900] C195
15) [241, 886, 192393] C3 x C195 92) [21377, 443, 964] C3 x C195
16) [257, 554, 26357] C3 x C195 ---) [26357, 277, 12593] C195
17) [257, 727, 62164] C3 x C195 ---) [15541, 1454, 279873] C195
18) [257, 610, 91997] C3 x C195 ---) [91997, 305, 257] C195
19) [257, 659, 20612] C3 x C195 ---) [5153, 1247, 16448] C195
20) [257, 3162, 31333] C3 x C195 ---) [31333, 1581, 617057] C3705
21) [257, 1262, 394049] C3 x C195 ---) [394049, 631, 1028] C195
22) [257, 975, 129652] C3 x C195 99) [32413, 1950, 432017] C3 x C195
23) [257, 2246, 455177] C3 x C195 ---) [455177, 1123, 201488] C195
24) [277, 6262, 7658073] C3 x C195 124) [850897, 3131, 536272] C3 x C195
25) [541, 2590, 1642401] C3 x C195 108) [182489, 1295, 8656] C3 x C195
26) [613, 1825, 720937] C3 x C195 79) [14713, 2471, 198612] C3 x C195
27) [733, 521, 53017] C3 x C195 ---) [53017, 1042, 59373] C15 x C195
28) [1069, 1182, 75617] C3 x C195 ---) [75617, 591, 68416] C3 x C3 x C195
29) [1949, 557, 65381] C3 x C195 ---) [65381, 1114, 48725] C3 x C3 x C195
30) [2609, 2694, 770809] C3 x C195 47) [4561, 1347, 260900] C3 x C195
31) [2677, 3057, 6653] C3 x C195 ---) [6653, 3593, 1416133] C195
32) [2677, 282, 9173] C3 x C195 ---) [9173, 141, 2677] C195
33) [2777, 3202, 685949] C3 x C195 ---) [5669, 1601, 469313] C195
34) [2777, 487, 41936] C3 x C195 ---) [2621, 974, 69425] C195
35) [2917, 1142, 279369] C3 x C195 ---) [3449, 571, 11668] C195
36) [2957, 1758, 15649] C3 x C195 83) [15649, 879, 189248] C3 x C195
37) [2969, 899, 35044] C3 x C195 ---) [8761, 1798, 668025] C3 x C3 x C1755
38) [3041, 2214, 9049] C3 x C195 ---) [9049, 1107, 304100] C3 x C1365
39) [3041, 2363, 1060672] C3 x C195 86) [16573, 4726, 1341081] C3 x C195
40) [3221, 2645, 395381] C3 x C195 61) [8069, 5237, 2013125] C3 x C195
41) [3229, 6049, 5736969] C3 x C195 ---) [13009, 4435, 464976] C195
42) [3593, 971, 191696] C3 x C195 72) [11981, 1942, 176057] C3 x C195
43) [3701, 277, 18257] C3 x C195 ---) [18257, 554, 3701] C3 x C3 x C195
44) [4241, 775, 64276] C3 x C195 85) [16069, 1550, 343521] C3 x C195
45) [4481, 3691, 259088] C3 x C195 ---) [16193, 7382, 12587129] C195
46) [4493, 2098, 651101] C3 x C195 ---) [5381, 1049, 112325] C195
47) [4561, 1347, 260900] C3 x C195 30) [2609, 2694, 770809] C3 x C195
48) [4637, 9134, 17222081] C3 x C195 89) [17921, 4567, 908852] C3 x C195
49) [4657, 1626, 642341] C3 x C195 76) [13109, 813, 4657] C3 x C195
50) [4729, 3242, 1700757] C3 x C195 ---) [2333, 1621, 231721] C195
51) [5081, 606, 10513] C3 x C195 ---) [10513, 303, 20324] C195
52) [5081, 4859, 5901200] C3 x C195 ---) [14753, 8203, 3983504] C195
53) [5281, 642, 81917] C3 x C195 ---) [677, 321, 5281] C195
54) [5297, 895, 92992] C3 x C195 ---) [1453, 1790, 429057] C195
55) [5477, 362, 10853] C3 x C195 ---) [10853, 181, 5477] C195
56) [5477, 2029, 962117] C3 x C195 ---) [5693, 4058, 268373] C195
57) [6053, 338, 4349] C3 x C195 ---) [4349, 169, 6053] C195
58) [6637, 738, 109613] C3 x C195 ---) [2237, 369, 6637] C195
59) [7481, 3371, 1043600] C3 x C195 ---) [2609, 2959, 748100] C195
60) [7673, 227, 10964] C3 x C195 ---) [2741, 454, 7673] C195
61) [8069, 5237, 2013125] C3 x C195 40) [3221, 2645, 395381] C3 x C195
62) [8581, 2705, 25101] C3 x C195 ---) [2789, 4461, 4539349] C195
63) [8837, 117, 1213] C3 x C195 ---) [1213, 234, 8837] C195
64) [9133, 2713, 1837809] C3 x C195 ---) [2521, 5159, 3653200] C195
65) [9293, 1114, 273077] C3 x C195 ---) [5573, 557, 9293] C195
66) [9413, 133, 2069] C3 x C195 ---) [2069, 266, 9413] C195
67) [10733, 4425, 4763677] C3 x C195 ---) [4957, 6021, 525917] C195
68) [10733, 1213, 43169] C3 x C195 ---) [881, 2426, 1298693] C195
69) [10733, 2813, 1954093] C3 x C195 ---) [5413, 5626, 96597] C195
70) [10949, 2685, 1668181] C3 x C195 ---) [4621, 5370, 536501] C195
71) [11777, 5950, 8662193] C3 x C195 ---) [5153, 2975, 47108] C195
72) [11981, 1942, 176057] C3 x C195 42) [3593, 971, 191696] C3 x C195
73) [12197, 2393, 1062653] C3 x C195 ---) [3677, 4786, 1475837] C195
74) [12269, 841, 26525] C3 x C195 ---) [1061, 1682, 601181] C195
75) [12821, 4645, 5981] C3 x C195 ---) [5981, 9290, 21552101] C195
76) [13109, 813, 4657] C3 x C195 49) [4657, 1626, 642341] C3 x C195
77) [13577, 971, 69392] C3 x C195 ---) [4337, 1942, 665273] C195
78) [14389, 549, 71753] C3 x C195 ---) [593, 1098, 14389] C195
79) [14713, 2471, 198612] C3 x C195 26) [613, 1825, 720937] C3 x C195
80) [15061, 765, 142541] C3 x C195 ---) [2909, 1530, 15061] C195
81) [15061, 2621, 1412425] C3 x C195 ---) [1153, 3599, 60244] C195
82) [15641, 899, 10448] C3 x C195 ---) [653, 1798, 766409] C195
83) [15649, 879, 189248] C3 x C195 36) [2957, 1758, 15649] C3 x C195
84) [15661, 3457, 2983797] C3 x C195 ---) [4093, 6914, 15661] C195
85) [16069, 1550, 343521] C3 x C195 44) [4241, 775, 64276] C3 x C195
86) [16573, 4726, 1341081] C3 x C195 39) [3041, 2363, 1060672] C3 x C195
87) [16673, 2070, 4153] C3 x C195 ---) [4153, 1035, 266768] C195
88) [17581, 1122, 244397] C3 x C195 ---) [677, 561, 17581] C195
89) [17921, 4567, 908852] C3 x C195 48) [4637, 9134, 17222081] C3 x C195
90) [18521, 5299, 6644800] C3 x C195 ---) [4153, 7431, 74084] C195
91) [20341, 1418, 421317] C3 x C195 ---) [277, 709, 20341] C195
92) [21377, 443, 964] C3 x C195 15) [241, 886, 192393] C3 x C195
93) [23297, 2039, 567616] C3 x C195 ---) [181, 1661, 209673] C195
94) [24001, 1002, 154997] C3 x C195 ---) [293, 501, 24001] C195
95) [26489, 1791, 628] C3 x C195 ---) [157, 1321, 238401] C195
96) [28657, 523, 3904] C3 x C195 ---) [61, 1046, 257913] C195
97) [31121, 439, 40400] C3 x C195 ---) [101, 878, 31121] C195
98) [32353, 722, 909] C3 x C195 ---) [101, 361, 32353] C195
99) [32413, 1950, 432017] C3 x C195 22) [257, 975, 129652] C3 x C195
100) [36677, 549, 66181] C3 x C195 11) [229, 1098, 36677] C3 x C195
101) [55229, 1181, 3509] C3 x C195 ---) [29, 821, 55229] C39
102) [83177, 307, 2768] C3 x C195 ---) [173, 614, 83177] C195
103) [103813, 1330, 26973] C3 x C195 ---) [37, 665, 103813] C39
104) [133097, 563, 45968] C3 x C195 ---) [17, 1126, 133097] C39
105) [147773, 1610, 56933] C3 x C195 ---) [197, 805, 147773] C195
106) [155809, 399, 848] C3 x C195 ---) [53, 798, 155809] C195
107) [179233, 3406, 32481] C3 x C195 ---) [401, 1703, 716932] C5 x C195
108) [182489, 1295, 8656] C3 x C195 25) [541, 2590, 1642401] C3 x C195
109) [195401, 443, 212] C3 x C195 ---) [53, 886, 195401] C195
110) [201937, 1303, 373968] C3 x C195 ---) [53, 2606, 201937] C195
111) [205357, 457, 873] C3 x C195 ---) [97, 914, 205357] C195
112) [232457, 739, 78416] C3 x C195 ---) [29, 1478, 232457] C195
113) [275449, 1451, 457488] C3 x C195 ---) [353, 2902, 275449] C195
114) [340709, 2338, 3725] C3 x C195 ---) [149, 1169, 340709] C195
115) [442721, 911, 96800] C3 x C195 ---) [8, 1822, 442721] C195
116) [448853, 749, 28037] C3 x C195 ---) [53, 1498, 448853] C195
117) [481177, 723, 10388] C3 x C195 ---) [53, 1446, 481177] C195
118) [506629, 773, 22725] C3 x C195 ---) [101, 1546, 506629] C195
119) [529313, 743, 5684] C3 x C195 ---) [29, 1486, 529313] C195
120) [557021, 785, 14801] C3 x C195 ---) [41, 1570, 557021] C195
121) [627217, 805, 5202] C3 x C195 ---) [8, 1610, 627217] C195
122) [757753, 2687, 100048] C3 x C195 ---) [37, 5245, 6819777] C195
123) [805081, 1019, 58320] C3 x C195 ---) [5, 1977, 805081] C195
124) [850897, 3131, 536272] C3 x C195 24) [277, 6262, 7658073] C3 x C195
125) [1005409, 3059, 77200] C3 x C195 ---) [193, 6118, 9048681] C195
126) [1030241, 1711, 474320] C3 x C195 ---) [5, 2053, 1030241] C195
127) [1056361, 2419, 1198800] C3 x C195 ---) [37, 4838, 1056361] C195
128) [1295809, 1183, 25920] C3 x C195 ---) [5, 2366, 1295809] C195
129) [1379953, 4043, 981568] C3 x C195 ---) [313, 8086, 12419577] C195
130) [1517161, 1731, 369800] C3 x C195 ---) [8, 3462, 1517161] C195
131) [1660873, 1289, 162] C3 x C195 ---) [8, 2578, 1660873] C195
132) [1680181, 1309, 8325] C3 x C195 ---) [37, 2618, 1680181] C195
133) [1943393, 1615, 166208] C3 x C195 5) [53, 3230, 1943393] C3 x C195
134) [1990249, 1427, 11520] C3 x C195 ---) [5, 2854, 1990249] C195
135) [2163401, 1699, 180800] C3 x C195 ---) [113, 3398, 2163401] C195
136) [2327497, 2083, 502848] C3 x C195 ---) [97, 4166, 2327497] C195
137) [2499449, 1643, 50000] C3 x C195 ---) [5, 3286, 2499449] C195
138) [2746889, 1667, 8000] C3 x C195 ---) [5, 3334, 2746889] C195
139) [3398489, 2267, 435200] C3 x C195 ---) [17, 4534, 3398489] C3 x C39
140) [3456073, 1891, 29952] C3 x C195 ---) [13, 3782, 3456073] C195
141) [3951161, 2731, 876800] C3 x C195 7) [137, 5462, 3951161] C3 x C195
142) [4113097, 2083, 56448] C3 x C195 ---) [8, 4166, 4113097] C195
143) [4121629, 2697, 788045] C3 x C195 ---) [5, 4121, 4121629] C195
144) [4828457, 2227, 32768] C3 x C195 ---) [8, 4454, 4828457] C195
145) [4880713, 2275, 73728] C3 x C195 ---) [8, 4550, 4880713] C195
146) [4888889, 2347, 154880] C3 x C195 ---) [5, 4694, 4888889] C195
147) [5611721, 2435, 79376] C3 x C195 ---) [41, 4870, 5611721] C195
148) [5691709, 3417, 1496045] C3 x C195 ---) [5, 4781, 5691709] C195
149) [5827709, 3673, 1915805] C3 x C195 ---) [5, 4829, 5827709] C195
150) [7656809, 2771, 5408] C3 x C195 ---) [8, 5542, 7656809] C195
151) [8481689, 3067, 231200] C3 x C195 ---) [8, 6134, 8481689] C195
152) [10821497, 3403, 189728] C3 x C195 ---) [8, 6806, 10821497] C195
153) [15802489, 3979, 7488] C3 x C195 4) [13, 7958, 15802489] C3 x C195
154) [26488409, 5147, 800] C3 x C195 1) [8, 10294, 26488409] C3 x C195