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 C2 x C54 non-normal (D4) quartic CM field invariants: 9088 fields

K Quartic invariants Cl(OK) Igusa invariants Kr Reflex invariants Cl(OKr) Igusa invariants
1) [5, 550, 65045] C2 x C54 ---) [65045, 275, 2645] C6 x C108
2) [5, 457, 50851] C2 x C54 ---) [203404, 914, 5445] C2 x C216
3) [5, 443, 40861] C2 x C54 ---) [40861, 231, 3125] C2 x C2 x C54
4) [5, 340, 26020] C2 x C54 ---) [6505, 170, 720] C2 x C108
5) [5, 2450, 1335005] C2 x C54 ---) [27245, 1225, 41405] C6 x C108
6) [5, 1770, 774405] C2 x C54 ---) [86045, 885, 2205] C6 x C108
7) [5, 3881, 3097589] C2 x C54 ---) [3097589, 1997, 222605] C2 x C2376
8) [5, 626, 97844] C2 x C54 ---) [24461, 482, 33620] C2 x C6 x C54
9) [5, 559, 73159] C2 x C54 ---) [292636, 1118, 19845] C2 x C108
10) [5, 2494, 1400129] C2 x C54 ---) [1400129, 1247, 38720] C2 x C108
11) [5, 561, 78019] C2 x C54 ---) [312076, 1122, 2645] C2 x C108
12) [5, 606, 91789] C2 x C54 8714) [91789, 303, 5] C2 x C54
13) [5, 1950, 766305] C2 x C54 ---) [85145, 975, 46080] C2 x C540
14) [5, 403, 37601] C2 x C54 8354) [37601, 241, 5120] C2 x C54
15) [5, 553, 64691] C2 x C54 ---) [258764, 1106, 47045] C2 x C2 x C54
16) [5, 546, 73684] C2 x C54 4145) [109, 442, 30420] C2 x C54
17) [5, 348, 27151] C2 x C54 ---) [108604, 696, 12500] C2 x C108
18) [5, 1725, 738945] C2 x C54 ---) [82105, 1215, 184320] C6 x C108
19) [5, 488, 58091] C2 x C54 ---) [232364, 976, 5780] C2 x C216
20) [5, 3529, 3111149] C2 x C54 ---) [3111149, 2593, 903125] C2 x C108
21) [5, 670, 90445] C2 x C54 ---) [90445, 335, 5445] C2 x C540
22) [5, 1705, 695945] C2 x C54 ---) [695945, 1475, 369920] C4 x C216
23) [5, 367, 33221] C2 x C54 8286) [33221, 299, 14045] C2 x C54
24) [5, 1605, 577305] C2 x C54 ---) [64145, 915, 64980] C2 x C108
25) [5, 736, 133619] C2 x C54 ---) [534476, 1472, 7220] C2 x C216
26) [5, 2769, 1889829] C2 x C54 8929) [209981, 1893, 423405] C2 x C54
27) [5, 1573, 608681] C2 x C54 ---) [608681, 1291, 264500] C6 x C216
28) [5, 624, 96219] C2 x C54 8411) [42764, 1248, 4500] C2 x C54
29) [5, 424, 44899] C2 x C54 ---) [179596, 848, 180] C2 x C1080
30) [5, 2337, 1362141] C2 x C54 8856) [151349, 1689, 372645] C2 x C54
31) [5, 2005, 1003645] C2 x C54 ---) [1003645, 1545, 345845] C2 x C2 x C216
32) [5, 1734, 648009] C2 x C54 ---) [72001, 867, 25920] C2 x C432
33) [5, 531, 61459] C2 x C54 ---) [245836, 1062, 36125] C2 x C216
34) [5, 3429, 2546109] C2 x C54 ---) [282901, 3273, 2041605] C2 x C108
35) [5, 629, 98699] C2 x C54 ---) [394796, 1258, 845] C2 x C108
36) [5, 423, 40381] C2 x C54 8383) [40381, 391, 28125] C2 x C54
37) [5, 312, 20131] C2 x C54 ---) [80524, 624, 16820] C2 x C216
38) [5, 2741, 1877909] C2 x C54 ---) [1877909, 2077, 609005] C2 x C2 x C54
39) [5, 2894, 2073329] C2 x C54 ---) [2073329, 1447, 5120] C12 x C432
40) [5, 866, 187169] C2 x C54 8902) [187169, 433, 80] C2 x C54
41) [5, 363, 27661] C2 x C54 ---) [27661, 191, 2205] C6 x C54
42) [5, 2578, 1660541] C2 x C54 ---) [1660541, 1289, 245] C4 x C108
43) [5, 298, 21076] C2 x C54 ---) [5269, 186, 3380] C2 x C270
44) [5, 459, 42769] C2 x C54 8412) [42769, 233, 2880] C2 x C54
45) [5, 415, 37445] C2 x C54 ---) [37445, 395, 29645] C2 x C108
46) [5, 515, 66095] C2 x C54 ---) [264380, 1030, 845] C2 x C108
47) [5, 1318, 433001] C2 x C54 ---) [433001, 659, 320] C2 x C2 x C54
48) [5, 1654, 596809] C2 x C54 ---) [596809, 827, 21780] C2 x C108
49) [5, 461, 47179] C2 x C54 ---) [188716, 922, 23805] C2 x C6 x C54
50) [5, 616, 88739] C2 x C54 ---) [7244, 1232, 24500] C6 x C54
51) [5, 352, 30131] C2 x C54 ---) [120524, 704, 3380] C2 x C108
52) [5, 1686, 623529] C2 x C54 ---) [69281, 843, 21780] C2 x C2 x C54
53) [5, 479, 56449] C2 x C54 8531) [56449, 393, 24500] C2 x C54
54) [5, 455, 47695] C2 x C54 ---) [190780, 910, 16245] C2 x C108
55) [5, 540, 59380] C2 x C54 ---) [14845, 270, 3380] C2 x C108
56) [5, 2810, 1973045] C2 x C54 ---) [1973045, 1405, 245] C4 x C216
57) [5, 634, 81884] C2 x C54 ---) [81884, 628, 78125] C2 x C756
58) [5, 821, 168359] C2 x C54 ---) [673436, 1642, 605] C2 x C108
59) [5, 746, 138809] C2 x C54 8839) [138809, 373, 80] C2 x C54
60) [5, 1569, 596529] C2 x C54 8596) [66281, 1023, 112500] C2 x C54
61) [5, 1645, 650945] C2 x C54 ---) [650945, 1055, 115520] C8 x C216
62) [5, 480, 56755] C2 x C54 ---) [227020, 960, 3380] C2 x C108
63) [5, 719, 128039] C2 x C54 ---) [512156, 1438, 4805] C2 x C108
64) [5, 470, 54980] C2 x C54 ---) [13745, 370, 20480] C2 x C108
65) [5, 546, 73249] C2 x C54 8644) [73249, 273, 320] C2 x C54
66) [5, 551, 68869] C2 x C54 ---) [68869, 507, 47045] C2 x C2 x C54
67) [5, 343, 26651] C2 x C54 ---) [106604, 686, 11045] C2 x C108
68) [5, 1717, 735661] C2 x C54 ---) [735661, 1329, 257645] C2 x C108
69) [5, 616, 94844] C2 x C54 ---) [94844, 308, 5] C6 x C108
70) [5, 3309, 2731069] C2 x C54 ---) [2731069, 2393, 748845] C2 x C2 x C54
71) [5, 2066, 1026589] C2 x C54 ---) [1026589, 1033, 10125] C2 x C108
72) [5, 380, 33895] C2 x C54 ---) [135580, 760, 8820] C2 x C540
73) [5, 560, 72955] C2 x C54 ---) [291820, 1120, 21780] C6 x C108
74) [5, 454, 50924] C2 x C54 ---) [50924, 368, 21125] C2 x C108
75) [5, 422, 36916] C2 x C54 ---) [9229, 414, 33620] C2 x C270
76) [5, 2125, 1052645] C2 x C54 ---) [1052645, 1285, 149645] C2 x C216
77) [5, 2669, 1778989] C2 x C54 ---) [1778989, 1953, 508805] C6 x C108
78) [5, 312, 23836] C2 x C54 ---) [23836, 156, 125] C2 x C108
79) [5, 442, 43396] C2 x C54 7662) [10849, 414, 32000] C2 x C54
80) [5, 1709, 601369] C2 x C54 ---) [601369, 1683, 557780] C2 x C540
81) [5, 2525, 1587605] C2 x C54 ---) [1587605, 1805, 417605] C8 x C216
82) [5, 448, 49196] C2 x C54 6052) [1004, 224, 245] C2 x C54
83) [5, 2809, 1767589] C2 x C54 ---) [1767589, 2613, 1265045] C2 x C2 x C702
84) [5, 433, 46871] C2 x C54 ---) [187484, 866, 5] C2 x C108
85) [5, 547, 71801] C2 x C54 8630) [71801, 349, 12500] C2 x C54
86) [5, 2874, 2034549] C2 x C54 8948) [226061, 1437, 7605] C2 x C54
87) [5, 2641, 1696189] C2 x C54 ---) [1696189, 1737, 330245] C6 x C756
88) [5, 430, 46045] C2 x C54 ---) [46045, 215, 45] C2 x C108
89) [5, 4109, 3694469] C2 x C54 ---) [3694469, 3893, 2865245] C2 x C216
90) [5, 551, 75889] C2 x C54 8656) [75889, 417, 24500] C2 x C54
91) [5, 430, 46220] C2 x C54 ---) [46220, 320, 14045] C6 x C108
92) [5, 1133, 295361] C2 x C54 ---) [2441, 671, 38720] C108
93) [5, 292, 20911] C2 x C54 ---) [83644, 584, 1620] C6 x C108
94) [5, 731, 108029] C2 x C54 8769) [108029, 727, 105125] C2 x C54
95) [5, 2890, 2085605] C2 x C54 ---) [2085605, 1445, 605] C4 x C432
96) [5, 2485, 1541045] C2 x C54 ---) [1541045, 1805, 429245] C6 x C216
97) [5, 2566, 1429769] C2 x C54 ---) [1429769, 1283, 54080] C2 x C108
98) [5, 571, 79409] C2 x C54 ---) [79409, 377, 15680] C2 x C270
99) [5, 4261, 4500749] C2 x C54 ---) [4500749, 2977, 1090445] C2 x C216
100) [5, 439, 47899] C2 x C54 ---) [191596, 878, 1125] C2 x C2 x C54
101) [5, 435, 46855] C2 x C54 ---) [187420, 870, 1805] C2 x C108
102) [5, 2002, 805981] C2 x C54 ---) [6661, 1001, 49005] C108
103) [5, 507, 53451] C2 x C54 8122) [23756, 1014, 43245] C2 x C54
104) [5, 3641, 2675189] C2 x C54 ---) [22109, 1837, 174845] C108
105) [5, 348, 25156] C2 x C54 ---) [6289, 174, 1280] C6 x C54
106) [5, 1653, 555901] C2 x C54 5678) [661, 841, 37845] C2 x C54
107) [5, 2385, 1391245] C2 x C54 ---) [1391245, 1985, 637245] C2 x C216
108) [5, 252, 15796] C2 x C54 7141) [3949, 126, 20] C2 x C54
109) [5, 1390, 390545] C2 x C54 ---) [390545, 695, 23120] C2 x C216
110) [5, 2054, 1052729] C2 x C54 ---) [1052729, 1027, 500] C2 x C108
111) [5, 699, 101349] C2 x C54 7690) [11261, 363, 7605] C2 x C54
112) [5, 553, 76451] C2 x C54 ---) [305804, 1106, 5] C2 x C2 x C54
113) [5, 646, 85724] C2 x C54 ---) [85724, 332, 6125] C6 x C108
114) [5, 407, 39701] C2 x C54 2551) [29, 259, 6845] C2 x C54
115) [5, 1414, 464569] C2 x C54 7582) [9481, 707, 8820] C2 x C54
116) [5, 496, 61459] C2 x C54 ---) [245836, 992, 180] C2 x C216
117) [5, 563, 79091] C2 x C54 ---) [316364, 1126, 605] C2 x C216
118) [5, 1257, 368001] C2 x C54 8392) [40889, 759, 52020] C2 x C54
119) [5, 2610, 1694205] C2 x C54 ---) [188245, 1305, 2205] C2 x C108
120) [5, 490, 55820] C2 x C54 ---) [55820, 440, 34445] C2 x C108
121) [5, 3269, 2633309] C2 x C54 ---) [53741, 2233, 588245] C2 x C540
122) [5, 631, 84689] C2 x C54 8688) [84689, 337, 7220] C2 x C54
123) [5, 686, 103604] C2 x C54 8169) [25901, 382, 10580] C2 x C54
124) [5, 535, 70355] C2 x C54 ---) [281420, 1070, 4805] C2 x C108
125) [5, 2169, 1032489] C2 x C54 ---) [114721, 1203, 103680] C2 x C108
126) [5, 1338, 443061] C2 x C54 8471) [49229, 669, 1125] C2 x C54
127) [5, 649, 104939] C2 x C54 ---) [419756, 1298, 1445] C6 x C108
128) [5, 562, 70961] C2 x C54 8627) [70961, 281, 2000] C2 x C54
129) [5, 566, 75884] C2 x C54 ---) [75884, 352, 12005] C2 x C108
130) [5, 307, 23501] C2 x C54 8113) [23501, 239, 8405] C2 x C54
131) [5, 2505, 1305405] C2 x C54 ---) [145045, 1305, 99405] C2 x C108
132) [5, 2369, 1323029] C2 x C54 ---) [2501, 2093, 764405] C2 x C216
133) [5, 2353, 1226621] C2 x C54 ---) [1226621, 1321, 129605] C2 x C108
134) [5, 432, 40876] C2 x C54 ---) [40876, 216, 1445] C2 x C216
135) [5, 292, 20596] C2 x C54 7270) [5149, 146, 180] C2 x C54
136) [5, 1401, 446049] C2 x C54 ---) [49561, 1287, 302580] C2 x C108
137) [5, 1174, 318649] C2 x C54 ---) [318649, 587, 6480] C2 x C216
138) [5, 3441, 2549709] C2 x C54 ---) [283301, 3297, 2080125] C2 x C864
139) [5, 440, 46955] C2 x C54 ---) [187820, 880, 5780] C2 x C108
140) [5, 2449, 1489049] C2 x C54 ---) [1489049, 1723, 369920] C2 x C108
141) [5, 1182, 342801] C2 x C54 ---) [38089, 591, 1620] C2 x C108
142) [5, 1305, 414945] C2 x C54 ---) [46105, 1095, 196020] C2 x C108
143) [5, 397, 38951] C2 x C54 ---) [155804, 794, 1805] C2 x C108
144) [5, 2274, 1292589] C2 x C54 8844) [143621, 1137, 45] C2 x C54
145) [5, 1245, 382545] C2 x C54 ---) [42505, 855, 87120] C2 x C108
146) [5, 571, 80959] C2 x C54 ---) [323836, 1142, 2205] C2 x C108
147) [5, 431, 40489] C2 x C54 8387) [40489, 237, 3920] C2 x C54
148) [5, 388, 35636] C2 x C54 ---) [8909, 194, 500] C6 x C54
149) [5, 559, 63269] C2 x C54 ---) [63269, 283, 4205] C2 x C378
150) [5, 2209, 1024889] C2 x C54 ---) [1024889, 1163, 81920] C2 x C108
151) [5, 851, 158939] C2 x C54 ---) [635756, 1702, 88445] C2 x C2 x C54
152) [5, 2057, 1057661] C2 x C54 ---) [8741, 1529, 320045] C108
153) [5, 400, 34555] C2 x C54 ---) [138220, 800, 21780] C2 x C108
154) [5, 2621, 1449449] C2 x C54 ---) [1449449, 1387, 118580] C2 x C108
155) [5, 1637, 593681] C2 x C54 ---) [593681, 919, 62720] C2 x C432
156) [5, 2045, 1036045] C2 x C54 ---) [1036045, 1425, 248645] C4 x C216
157) [5, 1286, 378169] C2 x C54 ---) [378169, 643, 8820] C2 x C108
158) [5, 611, 90329] C2 x C54 ---) [90329, 397, 16820] C2 x C702
159) [5, 671, 91109] C2 x C54 ---) [91109, 667, 88445] C2 x C378
160) [5, 2414, 1187729] C2 x C54 ---) [1187729, 1207, 67280] C2 x C216
161) [5, 1565, 550145] C2 x C54 ---) [550145, 895, 62720] C2 x C216
162) [5, 2073, 1069981] C2 x C54 ---) [1069981, 1481, 280845] C2 x C2 x C54
163) [5, 3189, 2541069] C2 x C54 ---) [282341, 2433, 844605] C2 x C432
164) [5, 1833, 703021] C2 x C54 ---) [703021, 961, 55125] C2 x C108
165) [5, 2065, 1065845] C2 x C54 ---) [1065845, 1565, 345845] C2 x C216
166) [5, 579, 83029] C2 x C54 ---) [83029, 403, 19845] C2 x C270
167) [5, 451, 44899] C2 x C54 ---) [179596, 902, 23805] C2 x C1080
168) [5, 1369, 456289] C2 x C54 ---) [456289, 903, 89780] C2 x C216
169) [5, 1461, 491769] C2 x C54 ---) [54641, 867, 64980] C2 x C216
170) [5, 448, 49676] C2 x C54 ---) [49676, 224, 125] C2 x C2 x C54
171) [5, 375, 32845] C2 x C54 ---) [32845, 335, 19845] C6 x C108
172) [5, 3026, 2144669] C2 x C54 ---) [7421, 1513, 36125] C2 x C108
173) [5, 736, 134924] C2 x C54 ---) [134924, 368, 125] C2 x C6 x C54
174) [5, 1022, 261041] C2 x C54 ---) [261041, 511, 20] C2 x C2 x C54
175) [5, 510, 64045] C2 x C54 ---) [64045, 255, 245] C2 x C108
176) [5, 1609, 563369] C2 x C54 ---) [563369, 883, 54080] C2 x C2 x C270
177) [5, 368, 32731] C2 x C54 ---) [130924, 736, 4500] C2 x C108
178) [5, 502, 56156] C2 x C54 ---) [56156, 284, 6125] C2 x C108
179) [5, 581, 76979] C2 x C54 7369) [6284, 1162, 29645] C2 x C54
180) [5, 302, 21181] C2 x C54 ---) [21181, 151, 405] C2 x C378
181) [5, 3245, 2632445] C2 x C54 ---) [2632445, 2425, 812045] C2 x C216
182) [5, 1905, 901645] C2 x C54 ---) [901645, 1345, 226845] C2 x C216
183) [5, 545, 73895] C2 x C54 ---) [295580, 1090, 1445] C2 x C108
184) [5, 2709, 1826869] C2 x C54 ---) [1826869, 1933, 477405] C2 x C108
185) [5, 530, 60980] C2 x C54 ---) [15245, 290, 5780] C2 x C216
186) [5, 523, 63731] C2 x C54 ---) [254924, 1046, 18605] C18 x C108
187) [5, 383, 36521] C2 x C54 8334) [36521, 301, 13520] C2 x C54
188) [5, 1602, 607981] C2 x C54 ---) [607981, 801, 8405] C2 x C2 x C54
189) [5, 411, 42219] C2 x C54 ---)