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 C775 non-normal (D4) quartic CM field invariants: 120 fields

K Quartic invariants Cl(OK) Igusa invariants Kr Reflex invariants Cl(OKr) Igusa invariants
1) [8, 5246, 6855041] C775 118) [6855041, 2623, 6272] C775
2) [8, 4798, 5754689] C775 117) [5754689, 2399, 128] C775
3) [13, 5406, 7143137] C775 120) [7143137, 2703, 40768] C775
4) [13, 5310, 6995777] C775 119) [6995777, 2655, 13312] C775
5) [17, 2398, 1044833] C775 112) [1044833, 1199, 98192] C775
6) [17, 1822, 477409] C775 106) [477409, 911, 88128] C775
7) [17, 1966, 939089] C775 111) [939089, 983, 6800] C775
8) [17, 2558, 1422593] C775 115) [1422593, 1279, 53312] C775
9) [37, 3678, 2775713] C775 ---) [2775713, 1839, 151552] C5 x C775
10) [41, 1366, 465833] C775 105) [465833, 683, 164] C775
11) [53, 4478, 3371393] C775 116) [3371393, 2239, 410432] C775
12) [53, 5102, 6168401] C775 ---) [6168401, 2551, 84800] C2325
13) [53, 2486, 1422937] C775 ---) [1422937, 1243, 30528] C2325
14) [73, 6198, 9487001] C775 ---) [9487001, 3099, 29200] C2325
15) [109, 2166, 1061273] C775 113) [1061273, 1083, 27904] C775
16) [113, 1342, 95873] C775 98) [95873, 671, 88592] C775
17) [113, 5510, 7127177] C775 ---) [7127177, 2755, 115712] C5425
18) [157, 3390, 1174913] C775 114) [1174913, 1695, 424528] C775
19) [157, 1686, 670457] C775 108) [670457, 843, 10048] C775
20) [269, 1294, 401393] C775 103) [401393, 647, 4304] C775
21) [277, 697, 120829] C775 ---) [120829, 1394, 2493] C5 x C775
22) [277, 1593, 622709] C775 107) [622709, 3186, 46813] C775
23) [293, 1846, 776921] C775 110) [776921, 923, 18752] C775
24) [317, 1294, 413537] C775 104) [413537, 647, 1268] C775
25) [317, 1562, 608693] C775 ---) [608693, 781, 317] C8525
26) [457, 2295, 1220672] C775 94) [19073, 2683, 1756708] C775
27) [461, 1713, 733477] C775 109) [733477, 3426, 461] C775
28) [569, 1462, 452425] C775 ---) [18097, 731, 20484] C2325
29) [593, 1042, 269069] C775 100) [269069, 521, 593] C775
30) [677, 1190, 310697] C775 101) [310697, 595, 10832] C775
31) [937, 1226, 342037] C775 102) [342037, 613, 8433] C775
32) [1153, 4415, 652788] C775 91) [18133, 2545, 1578457] C775
33) [1201, 1526, 409225] C775 ---) [16369, 763, 43236] C2325
34) [1549, 633, 81197] C775 97) [81197, 1266, 75901] C775
35) [2017, 783, 128564] C775 96) [32141, 1566, 98833] C775
36) [2053, 2614, 525721] C775 76) [10729, 1307, 295632] C775
37) [2389, 3489, 362225] C775 81) [14489, 6335, 611584] C775
38) [2437, 2341, 443401] C775 ---) [9049, 4682, 3706677] C5425
39) [2441, 6994, 11438125] C775 92) [18301, 3497, 197721] C775
40) [3109, 2989, 1486593] C775 ---) [18353, 5978, 2987749] C5 x C775
41) [3209, 2050, 10909] C775 ---) [10909, 1025, 259929] C5 x C775
42) [3257, 635, 34852] C775 ---) [8713, 1270, 263817] C2325
43) [3301, 3753, 3223337] C775 93) [19073, 7506, 1191661] C775
44) [3313, 2399, 1000656] C775 ---) [6949, 4798, 1752577] C5 x C775
45) [3413, 5013, 4397713] C775 83) [15217, 6327, 873728] C775
46) [3581, 5093, 16481] C775 ---) [16481, 6167, 6932816] C2325
47) [3593, 3751, 3193232] C775 52) [4073, 2675, 1739012] C775
48) [3613, 6229, 847357] C775 90) [17293, 7145, 5495373] C775
49) [3709, 4273, 884377] C775 65) [5233, 2863, 59344] C775
50) [3733, 3918, 911009] C775 72) [7529, 1959, 731668] C775
51) [4021, 6894, 4097153] C775 80) [14177, 3447, 1946164] C775
52) [4073, 2675, 1739012] C775 47) [3593, 3751, 3193232] C775
53) [4129, 354, 14813] C775 82) [14813, 177, 4129] C775
54) [4513, 1879, 556596] C775 84) [15461, 3758, 1304257] C775
55) [4621, 6210, 4299149] C775 78) [11909, 3105, 1335469] C775
56) [4721, 867, 158416] C775 74) [9901, 1734, 118025] C775
57) [4789, 4213, 547477] C775 77) [11173, 7381, 2533381] C775
58) [4789, 1518, 499457] C775 75) [10193, 759, 19156] C775
59) [4813, 833, 172269] C775 95) [19141, 1666, 4813] C775
60) [4957, 1214, 51201] C775 70) [5689, 607, 79312] C775
61) [4973, 4317, 4508689] C775 85) [15601, 8634, 601733] C775
62) [4993, 3331, 465876] C775 79) [12941, 6662, 9232057] C775
63) [5009, 4759, 371264] C775 71) [5801, 3115, 2424356] C775
64) [5189, 2109, 425725] C775 89) [17029, 4218, 2744981] C775
65) [5233, 2863, 59344] C775 49) [3709, 4273, 884377] C775
66) [5393, 2479, 68116] C775 88) [17029, 4958, 5872977] C775
67) [5441, 1351, 63188] C775 86) [15797, 2702, 1572449] C775
68) [5573, 4233, 2772841] C775 73) [7681, 5307, 356672] C775
69) [5669, 9137, 4645097] C775 87) [16073, 5159, 6553364] C775
70) [5689, 607, 79312] C775 60) [4957, 1214, 51201] C775
71) [5801, 3115, 2424356] C775 63) [5009, 4759, 371264] C775
72) [7529, 1959, 731668] C775 50) [3733, 3918, 911009] C775
73) [7681, 5307, 356672] C775 68) [5573, 4233, 2772841] C775
74) [9901, 1734, 118025] C775 56) [4721, 867, 158416] C775
75) [10193, 759, 19156] C775 58) [4789, 1518, 499457] C775
76) [10729, 1307, 295632] C775 36) [2053, 2614, 525721] C775
77) [11173, 7381, 2533381] C775 57) [4789, 4213, 547477] C775
78) [11909, 3105, 1335469] C775 55) [4621, 6210, 4299149] C775
79) [12941, 6662, 9232057] C775 62) [4993, 3331, 465876] C775
80) [14177, 3447, 1946164] C775 51) [4021, 6894, 4097153] C775
81) [14489, 6335, 611584] C775 37) [2389, 3489, 362225] C775
82) [14813, 177, 4129] C775 53) [4129, 354, 14813] C775
83) [15217, 6327, 873728] C775 45) [3413, 5013, 4397713] C775
84) [15461, 3758, 1304257] C775 54) [4513, 1879, 556596] C775
85) [15601, 8634, 601733] C775 61) [4973, 4317, 4508689] C775
86) [15797, 2702, 1572449] C775 67) [5441, 1351, 63188] C775
87) [16073, 5159, 6553364] C775 69) [5669, 9137, 4645097] C775
88) [17029, 4958, 5872977] C775 66) [5393, 2479, 68116] C775
89) [17029, 4218, 2744981] C775 64) [5189, 2109, 425725] C775
90) [17293, 7145, 5495373] C775 48) [3613, 6229, 847357] C775
91) [18133, 2545, 1578457] C775 32) [1153, 4415, 652788] C775
92) [18301, 3497, 197721] C775 39) [2441, 6994, 11438125] C775
93) [19073, 7506, 1191661] C775 43) [3301, 3753, 3223337] C775
94) [19073, 2683, 1756708] C775 26) [457, 2295, 1220672] C775
95) [19141, 1666, 4813] C775 59) [4813, 833, 172269] C775
96) [32141, 1566, 98833] C775 35) [2017, 783, 128564] C775
97) [81197, 1266, 75901] C775 34) [1549, 633, 81197] C775
98) [95873, 671, 88592] C775 16) [113, 1342, 95873] C775
99) [133417, 377, 2178] C775 ---) [8, 754, 133417] C31
100) [269069, 521, 593] C775 29) [593, 1042, 269069] C775
101) [310697, 595, 10832] C775 30) [677, 1190, 310697] C775
102) [342037, 613, 8433] C775 31) [937, 1226, 342037] C775
103) [401393, 647, 4304] C775 20) [269, 1294, 401393] C775
104) [413537, 647, 1268] C775 24) [317, 1294, 413537] C775
105) [465833, 683, 164] C775 10) [41, 1366, 465833] C775
106) [477409, 911, 88128] C775 6) [17, 1822, 477409] C775
107) [622709, 3186, 46813] C775 22) [277, 1593, 622709] C775
108) [670457, 843, 10048] C775 19) [157, 1686, 670457] C775
109) [733477, 3426, 461] C775 27) [461, 1713, 733477] C775
110) [776921, 923, 18752] C775 23) [293, 1846, 776921] C775
111) [939089, 983, 6800] C775 7) [17, 1966, 939089] C775
112) [1044833, 1199, 98192] C775 5) [17, 2398, 1044833] C775
113) [1061273, 1083, 27904] C775 15) [109, 2166, 1061273] C775
114) [1174913, 1695, 424528] C775 18) [157, 3390, 1174913] C775
115) [1422593, 1279, 53312] C775 8) [17, 2558, 1422593] C775
116) [3371393, 2239, 410432] C775 11) [53, 4478, 3371393] C775
117) [5754689, 2399, 128] C775 2) [8, 4798, 5754689] C775
118) [6855041, 2623, 6272] C775 1) [8, 5246, 6855041] C775
119) [6995777, 2655, 13312] C775 4) [13, 5310, 6995777] C775
120) [7143137, 2703, 40768] C775 3) [13, 5406, 7143137] C775