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 C111 non-normal (D4) quartic CM field invariants: 190 fields

K Quartic invariants Cl(OK) Igusa invariants Kr Reflex invariants Cl(OKr) Igusa invariants
1) [5, 5654, 7973929] C3 x C111 188) [7973929, 2827, 4500] C3 x C111
2) [5, 2217, 1195561] C3 x C111 173) [1195561, 1459, 233280] C3 x C111
3) [5, 7774, 14781089] C3 x C111 190) [14781089, 3887, 81920] C3 x C111
4) [8, 7814, 14969737] C3 x C111 ---) [14969737, 3907, 73728] C3 x C3 x C111
5) [8, 8198, 16455689] C3 x C111 ---) [16455689, 4099, 86528] C3 x C3 x C111
6) [13, 4478, 4893313] C3 x C111 186) [4893313, 2239, 29952] C3 x C111
7) [13, 5294, 6639697] C3 x C111 187) [6639697, 2647, 91728] C3 x C111
8) [17, 6758, 10682153] C3 x C111 ---) [10682153, 3379, 183872] C3 x C3 x C333
9) [17, 8230, 9256297] C3 x C111 189) [9256297, 4115, 1919232] C3 x C111
10) [37, 2574, 972017] C3 x C111 167) [972017, 1287, 171088] C3 x C111
11) [41, 646, 51193] C3 x C111 139) [51193, 323, 13284] C3 x C111
12) [41, 1514, 394453] C3 x C111 155) [394453, 757, 44649] C3 x C111
13) [41, 3862, 3634297] C3 x C111 185) [3634297, 1931, 23616] C3 x C111
14) [53, 2990, 593297] C3 x C111 157) [593297, 1495, 410432] C3 x C111
15) [113, 2510, 1573217] C3 x C111 ---) [1573217, 1255, 452] C3 x C3 x C111
16) [229, 1794, 34253] C3 x C111 129) [34253, 897, 192589] C3 x C111
17) [229, 477, 26597] C3 x C111 ---) [26597, 954, 121141] C111
18) [229, 425, 44641] C3 x C111 138) [44641, 850, 2061] C3 x C111
19) [229, 441, 47189] C3 x C111 ---) [47189, 882, 5725] C111
20) [229, 773, 87037] C3 x C111 ---) [87037, 1546, 249381] C111
21) [229, 1842, 847325] C3 x C111 ---) [33893, 921, 229] C111
22) [229, 317, 12241] C3 x C111 ---) [12241, 634, 51525] C111
23) [257, 730, 8837] C3 x C111 88) [8837, 365, 31097] C3 x C111
24) [257, 179, 6404] C3 x C111 ---) [1601, 358, 6425] C777
25) [257, 914, 35117] C3 x C111 ---) [35117, 457, 43433] C111
26) [257, 866, 13757] C3 x C111 ---) [13757, 433, 43433] C111
27) [281, 2363, 115636] C3 x C111 125) [28909, 1785, 789329] C3 x C111
28) [349, 5833, 913041] C3 x C111 144) [101449, 4787, 22336] C3 x C111
29) [353, 2150, 794153] C3 x C111 163) [794153, 1075, 90368] C3 x C111
30) [421, 1170, 340541] C3 x C111 153) [340541, 585, 421] C3 x C111
31) [449, 1354, 413429] C3 x C111 156) [413429, 677, 11225] C3 x C111
32) [457, 1291, 383652] C3 x C111 99) [10657, 2107, 148068] C3 x C111
33) [569, 2698, 1817525] C3 x C111 142) [72701, 1349, 569] C3 x C111
34) [569, 3254, 1736729] C3 x C111 ---) [1736729, 1627, 227600] C3 x C777
35) [653, 517, 65353] C3 x C111 ---) [65353, 1034, 5877] C3 x C1221
36) [733, 405, 10037] C3 x C111 ---) [10037, 810, 123877] C111
37) [761, 1218, 2557] C3 x C111 55) [2557, 609, 92081] C3 x C111
38) [761, 1018, 109925] C3 x C111 ---) [4397, 509, 37289] C111
39) [761, 598, 40697] C3 x C111 ---) [40697, 299, 12176] C777
40) [761, 2566, 866825] C3 x C111 ---) [34673, 1283, 194816] C111
41) [797, 722, 127133] C3 x C111 146) [127133, 361, 797] C3 x C111
42) [1193, 2842, 1632709] C3 x C111 93) [9661, 1421, 96633] C3 x C111
43) [1229, 129, 3853] C3 x C111 ---) [3853, 258, 1229] C111
44) [1229, 653, 69425] C3 x C111 59) [2777, 1306, 148709] C3 x C111
45) [1489, 1606, 549513] C3 x C111 ---) [61057, 803, 23824] C111
46) [1861, 2721, 231425] C3 x C111 91) [9257, 4183, 2687284] C3 x C111
47) [1949, 1161, 79225] C3 x C111 63) [3169, 2322, 1031021] C3 x C111
48) [1949, 394, 31013] C3 x C111 127) [31013, 197, 1949] C3 x C111
49) [2089, 795, 132416] C3 x C111 ---) [2069, 1590, 102361] C111
50) [2137, 4311, 4555892] C3 x C111 ---) [9413, 2945, 1130473] C3 x C3 x C111
51) [2213, 1857, 104713] C3 x C111 ---) [2137, 1279, 318672] C111
52) [2437, 4261, 1467801] C3 x C111 117) [18121, 5183, 4718032] C3 x C111
53) [2441, 1247, 119632] C3 x C111 82) [7477, 2494, 1076481] C3 x C111
54) [2549, 705, 16561] C3 x C111 110) [16561, 1410, 430781] C3 x C111
55) [2557, 609, 92081] C3 x C111 37) [761, 1218, 2557] C3 x C111
56) [2657, 3711, 1975552] C3 x C111 84) [7717, 3265, 23913] C3 x C111
57) [2753, 6127, 9186128] C3 x C111 100) [11717, 3673, 2315273] C3 x C111
58) [2777, 1015, 6932] C3 x C111 ---) [1733, 2030, 1002497] C111
59) [2777, 1306, 148709] C3 x C111 44) [1229, 653, 69425] C3 x C111
60) [2789, 401, 22769] C3 x C111 ---) [22769, 802, 69725] C3 x C3 x C111
61) [2801, 370, 23021] C3 x C111 119) [23021, 185, 2801] C3 x C111
62) [2917, 2881, 26577] C3 x C111 ---) [2953, 2635, 105012] C111
63) [3169, 2322, 1031021] C3 x C111 47) [1949, 1161, 79225] C3 x C111
64) [3221, 1229, 144893] C3 x C111 ---) [2957, 2458, 930869] C111
65) [3229, 521, 2473] C3 x C111 ---) [2473, 1042, 261549] C111
66) [3229, 977, 5337] C3 x C111 ---) [593, 999, 206656] C111
67) [3229, 4037, 231025] C3 x C111 ---) [9241, 4927, 2906100] C111
68) [3413, 3901, 2875261] C3 x C111 94) [9949, 4689, 4180925] C3 x C111
69) [3877, 1746, 2237] C3 x C111 ---) [2237, 873, 189973] C111
70) [4001, 4518, 1006057] C3 x C111 ---) [5953, 2259, 1024256] C111
71) [4093, 4394, 95301] C3 x C111 98) [10589, 2197, 1182877] C3 x C111
72) [4253, 3517, 2198129] C3 x C111 81) [6089, 3859, 68048] C3 x C111
73) [4373, 5205, 4935253] C3 x C111 113) [17077, 8025, 214277] C3 x C111
74) [4481, 1199, 35648] C3 x C111 ---) [557, 1601, 219569] C111
75) [4517, 1693, 625093] C3 x C111 103) [12757, 3386, 365877] C3 x C111
76) [4549, 7281, 5036609] C3 x C111 92) [9521, 3815, 18196] C3 x C111
77) [4729, 5006, 136225] C3 x C111 ---) [5449, 2503, 1532196] C111
78) [5077, 1033, 113193] C3 x C111 ---) [12577, 2066, 614317] C3 x C3 x C111
79) [5077, 7213, 12335409] C3 x C111 112) [16921, 7631, 12692500] C3 x C111
80) [5477, 2605, 972173] C3 x C111 ---) [2693, 3169, 5477] C111
81) [6089, 3859, 68048] C3 x C111 72) [4253, 3517, 2198129] C3 x C111
82) [7477, 2494, 1076481] C3 x C111 53) [2441, 1247, 119632] C3 x C111
83) [7673, 427, 43664] C3 x C111 ---) [2729, 854, 7673] C111
84) [7717, 3265, 23913] C3 x C111 56) [2657, 3711, 1975552] C3 x C111
85) [8017, 111, 1076] C3 x C111 ---) [269, 222, 8017] C111
86) [8017, 5227, 6491664] C3 x C111 ---) [5009, 3903, 801700] C111
87) [8581, 1245, 385361] C3 x C111 ---) [401, 1967, 858100] C555
88) [8837, 365, 31097] C3 x C111 23) [257, 730, 8837] C3 x C111
89) [8837, 1729, 727477] C3 x C111 ---) [757, 2265, 433013] C111
90) [9133, 757, 122713] C3 x C111 ---) [73, 475, 36532] C111
91) [9257, 4183, 2687284] C3 x C111 46) [1861, 2721, 231425] C3 x C111
92) [9521, 3815, 18196] C3 x C111 76) [4549, 7281, 5036609] C3 x C111
93) [9661, 1421, 96633] C3 x C111 42) [1193, 2842, 1632709] C3 x C111
94) [9949, 4689, 4180925] C3 x C111 68) [3413, 3901, 2875261] C3 x C111
95) [10069, 1906, 867933] C3 x C111 ---) [797, 953, 10069] C111
96) [10333, 6649, 5345901] C3 x C111 ---) [4909, 4121, 258325] C111
97) [10457, 1679, 388436] C3 x C111 ---) [269, 893, 10457] C111
98) [10589, 2197, 1182877] C3 x C111 71) [4093, 4394, 95301] C3 x C111
99) [10657, 2107, 148068] C3 x C111 32) [457, 1291, 383652] C3 x C111
100) [11717, 3673, 2315273] C3 x C111 57) [2753, 6127, 9186128] C3 x C111
101) [11789, 549, 1669] C3 x C111 ---) [1669, 1098, 294725] C111
102) [12197, 545, 46813] C3 x C111 ---) [277, 1090, 109773] C111
103) [12757, 3386, 365877] C3 x C111 75) [4517, 1693, 625093] C3 x C111
104) [15193, 554, 15957] C3 x C111 ---) [197, 277, 15193] C111
105) [15641, 1006, 2753] C3 x C111 ---) [2753, 503, 62564] C111
106) [15881, 4807, 2882500] C3 x C111 ---) [1153, 2463, 63524] C111
107) [16141, 529, 65925] C3 x C111 ---) [293, 1058, 16141] C111
108) [16477, 1721, 406801] C3 x C111 ---) [769, 3442, 1334637] C111
109) [16481, 3095, 1204004] C3 x C111 ---) [569, 2275, 1054784] C111
110) [16561, 1410, 430781] C3 x C111 54) [2549, 705, 16561] C3 x C111
111) [16661, 778, 84677] C3 x C111 ---) [293, 389, 16661] C111
112) [16921, 7631, 12692500] C3 x C111 79) [5077, 7213, 12335409] C3 x C111
113) [17077, 8025, 214277] C3 x C111 73) [4373, 5205, 4935253] C3 x C111
114) [17581, 1850, 222709] C3 x C111 ---) [421, 925, 158229] C111
115) [17581, 802, 90477] C3 x C111 ---) [1117, 401, 17581] C111
116) [17609, 1394, 415373] C3 x C111 ---) [173, 697, 17609] C111
117) [18121, 5183, 4718032] C3 x C111 52) [2437, 4261, 1467801] C3 x C111
118) [18541, 3770, 2885749] C3 x C111 ---) [829, 1885, 166869] C111
119) [23021, 185, 2801] C3 x C111 61) [2801, 370, 23021] C3 x C111
120) [23297, 1159, 50432] C3 x C111 ---) [197, 2213, 1141553] C111
121) [23957, 405, 35017] C3 x C111 ---) [97, 810, 23957] C111
122) [25301, 1173, 337657] C3 x C111 ---) [97, 1383, 404816] C111
123) [25717, 738, 33293] C3 x C111 ---) [197, 369, 25717] C111
124) [25981, 193, 2817] C3 x C111 ---) [313, 386, 25981] C111
125) [28909, 1785, 789329] C3 x C111 27) [281, 2363, 115636] C3 x C111
126) [30677, 1597, 16393] C3 x C111 ---) [97, 1047, 122708] C111
127) [31013, 197, 1949] C3 x C111 48) [1949, 394, 31013] C3 x C111
128) [31793, 1282, 283709] C3 x C111 ---) [101, 641, 31793] C111
129) [34253, 897, 192589] C3 x C111 16) [229, 1794, 34253] C3 x C111
130) [34877, 1681, 181] C3 x C111 ---) [181, 1893, 871925] C111
131) [35597, 825, 161257] C3 x C111 ---) [73, 1650, 35597] C111
132) [36469, 1702, 140697] C3 x C111 ---) [193, 851, 145876] C111
133) [38921, 227, 3152] C3 x C111 ---) [197, 454, 38921] C111
134) [38953, 2459, 1034496] C3 x C111 ---) [449, 4071, 3895300] C111
135) [41381, 1822, 167825] C3 x C111 ---) [137, 911, 165524] C111
136) [42073, 2498, 45373] C3 x C111 ---) [157, 1249, 378657] C111
137) [43577, 267, 6928] C3 x C111 ---) [433, 534, 43577] C111
138) [44641, 850, 2061] C3 x C111 18) [229, 425, 44641] C3 x C111
139) [51193, 323, 13284] C3 x C111 11) [41, 646, 51193] C3 x C111
140) [63317, 253, 173] C3 x C111 ---) [173, 506, 63317] C111
141) [67493, 1138, 53789] C3 x C111 ---) [149, 569, 67493] C111
142) [72701, 1349, 569] C3 x C111 33) [569, 2698, 1817525] C3 x C111
143) [74897, 3659, 182672] C3 x C111 ---) [233, 3179, 1198352] C111
144) [101449, 4787, 22336] C3 x C111 28) [349, 5833, 913041] C3 x C111
145) [122449, 357, 1250] C3 x C111 ---) [8, 714, 122449] C111
146) [127133, 361, 797] C3 x C111 41) [797, 722, 127133] C3 x C111
147) [149921, 2711, 848] C3 x C111 ---) [53, 2201, 149921] C111
148) [155201, 1979, 9104] C3 x C111 ---) [569, 3958, 3880025] C111
149) [199961, 475, 6416] C3 x C111 ---) [401, 950, 199961] C555
150) [264637, 2146, 92781] C3 x C111 ---) [61, 1073, 264637] C111
151) [323377, 607, 11268] C3 x C111 ---) [313, 1214, 323377] C111
152) [338753, 607, 7424] C3 x C111 ---) [29, 1214, 338753] C111
153) [340541, 585, 421] C3 x C111 30) [421, 1170, 340541] C3 x C111
154) [360193, 605, 1458] C3 x C111 ---) [8, 1210, 360193] C111
155) [394453, 757, 44649] C3 x C111 12) [41, 1514, 394453] C3 x C111
156) [413429, 677, 11225] C3 x C111 31) [449, 1354, 413429] C3 x C111
157) [593297, 1495, 410432] C3 x C111 14) [53, 2990, 593297] C3 x C111
158) [617689, 883, 40500] C3 x C111 ---) [5, 1749, 617689] C111
159) [642197, 813, 4693] C3 x C111 ---) [13, 1626, 642197] C111
160) [733561, 1291, 233280] C3 x C111 ---) [5, 1713, 733561] C111
161) [740581, 869, 3645] C3 x C111 ---) [5, 1738, 740581] C111
162) [790649, 907, 8000] C3 x C111 ---) [5, 1814, 790649] C111
163) [794153, 1075, 90368] C3 x C111 29) [353, 2150, 794153] C3 x C111
164) [888761, 971, 13520] C3 x C111 ---) [5, 1942, 888761] C111
165) [943289, 1003, 15680] C3 x C111 ---) [5, 2006, 943289] C111
166) [966209, 983, 20] C3 x C111 ---) [5, 1966, 966209] C111
167) [972017, 1287, 171088] C3 x C111 10) [37, 2574, 972017] C3 x C111
168) [1000409, 1403, 242000] C3 x C111 ---) [5, 2009, 1000409] C111
169) [1068217, 2155, 893952] C3 x C111 ---) [97, 4310, 1068217] C111
170) [1148089, 1483, 262800] C3 x C111 ---) [73, 2966, 1148089] C111
171) [1190953, 1099, 4212] C3 x C111 ---) [13, 2198, 1190953] C111
172) [1195421, 1529, 285605] C3 x C111 ---) [5, 2197, 1195421] C111
173) [1195561, 1459, 233280] C3 x C111 2) [5, 2217, 1195561] C3 x C111
174) [1197829, 1653, 383645] C3 x C111 ---) [5, 2189, 1197829] C111
175) [1294169, 1243, 62720] C3 x C111 ---) [5, 2486, 1294169] C111
176) [1467157, 1213, 1053] C3 x C111 ---) [13, 2426, 1467157] C111
177) [1499273, 1225, 338] C3 x C111 ---) [8, 2450, 1499273] C111
178) [1527289, 1291, 34848] C3 x C111 ---) [8, 2582, 1527289] C111
179) [1581869, 1313, 35525] C3 x C111 ---) [29, 2626, 1581869] C111
180) [1750409, 1603, 204800] C3 x C111 ---) [8, 3206, 1750409] C111
181) [1976809, 1411, 3528] C3 x C111 ---) [8, 2822, 1976809] C111
182) [2610137, 1627, 9248] C3 x C111 ---) [8, 3254, 2610137] C111
183) [2687609, 1697, 48050] C3 x C111 ---) [8, 3394, 2687609] C111
184) [3214949, 2773, 1118645] C3 x C111 ---) [5, 3589, 3214949] C111
185) [3634297, 1931, 23616] C3 x C111 13) [41, 3862, 3634297] C3 x C111
186) [4893313, 2239, 29952] C3 x C111 6) [13, 4478, 4893313] C3 x C111
187) [6639697, 2647, 91728] C3 x C111 7) [13, 5294, 6639697] C3 x C111
188) [7973929, 2827, 4500] C3 x C111 1) [5, 5654, 7973929] C3 x C111
189) [9256297, 4115, 1919232] C3 x C111 9) [17, 8230, 9256297] C3 x C111
190) [14781089, 3887, 81920] C3 x C111 3) [5, 7774, 14781089] C3 x C111