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 C777 non-normal (D4) quartic CM field invariants: 205 fields

K Quartic invariants Cl(OK) Igusa invariants Kr Reflex invariants Cl(OKr) Igusa invariants
1) [5, 6262, 9800281] C777 ---) [9800281, 3131, 720] C3 x C777
2) [8, 3998, 2243809] C777 192) [2243809, 1999, 438048] C777
3) [13, 9381, 21821309] C777 ---) [21821309, 15653, 12156157] C7 x C10101
4) [13, 10617, 28180013] C777 ---) [28180013, 18557, 22685533] C3 x C777
5) [13, 5574, 7746569] C777 204) [7746569, 2787, 5200] C777
6) [29, 4910, 5936081] C777 ---) [5936081, 2455, 22736] C3 x C777
7) [29, 3262, 2613761] C777 193) [2613761, 1631, 11600] C777
8) [73, 2094, 180497] C777 164) [180497, 1047, 228928] C777
9) [73, 2126, 457201] C777 176) [457201, 1063, 168192] C777
10) [89, 1710, 41809] C777 154) [41809, 855, 172304] C777
11) [97, 3526, 3052297] C777 197) [3052297, 1763, 13968] C777
12) [97, 702, 116993] C777 161) [116993, 351, 1552] C777
13) [101, 2614, 777433] C777 184) [777433, 1307, 232704] C777
14) [173, 1741, 757381] C777 183) [757381, 3482, 1557] C777
15) [197, 2150, 1105193] C777 189) [1105193, 1075, 12608] C777
16) [229, 534, 56633] C777 ---) [56633, 267, 3664] C259
17) [229, 558, 74177] C777 ---) [74177, 279, 916] C259
18) [229, 1306, 22453] C777 ---) [22453, 653, 100989] C259
19) [233, 4390, 4683817] C777 201) [4683817, 2195, 33552] C777
20) [233, 4742, 5561993] C777 ---) [5561993, 2371, 14912] C3 x C777
21) [257, 450, 49597] C777 ---) [49597, 225, 257] C259
22) [269, 2326, 922169] C777 186) [922169, 1163, 107600] C777
23) [457, 906, 203381] C777 166) [203381, 453, 457] C777
24) [509, 1462, 241177] C777 ---) [241177, 731, 73296] C14763
25) [601, 1398, 17417] C777 ---) [17417, 699, 117796] C3 x C777
26) [641, 2135, 1054784] C777 ---) [16481, 2899, 1602500] C3 x C777
27) [653, 1006, 211217] C777 167) [211217, 503, 10448] C777
28) [761, 1018, 12517] C777 ---) [12517, 509, 61641] C259
29) [761, 806, 52825] C777 ---) [2113, 403, 27396] C259
30) [821, 1286, 400313] C777 174) [400313, 643, 3284] C777
31) [929, 775, 131344] C777 104) [8209, 1550, 75249] C777
32) [997, 1293, 405749] C777 175) [405749, 2586, 48853] C777
33) [1153, 1667, 659844] C777 ---) [18329, 3334, 139513] C3 x C3885
34) [1193, 1759, 556096] C777 ---) [8689, 3339, 2524388] C3885
35) [1229, 1981, 118025] C777 ---) [4721, 1807, 78656] C259
36) [1249, 1143, 236372] C777 ---) [59093, 2286, 360961] C3 x C777
37) [1409, 3739, 42628] C777 118) [10657, 2019, 952484] C777
38) [1433, 1235, 37028] C777 111) [9257, 2470, 1377113] C777
39) [1597, 705, 104693] C777 ---) [104693, 1410, 78253] C3 x C777
40) [1601, 358, 6425] C777 ---) [257, 179, 6404] C3 x C111
41) [1777, 450, 43517] C777 156) [43517, 225, 1777] C777
42) [2017, 1322, 41589] C777 74) [4621, 661, 98833] C777
43) [2029, 578, 10477] C777 ---) [10477, 289, 18261] C111
44) [2053, 6045, 5932313] C777 139) [16433, 4187, 1387828] C777
45) [2089, 3191, 59188] C777 ---) [14797, 5177, 5868001] C259
46) [2393, 4174, 1905137] C777 ---) [11273, 2087, 612608] C3885
47) [2417, 3823, 607808] C777 114) [9497, 3115, 1169828] C777
48) [2557, 1329, 440921] C777 ---) [2609, 2511, 10228] C259
49) [2593, 6043, 255568] C777 138) [15973, 4513, 2180713] C777
50) [2609, 2758, 858041] C777 53) [2969, 1379, 260900] C777
51) [2689, 598, 46377] C777 82) [5153, 299, 10756] C777
52) [2749, 4397, 98937] C777 122) [10993, 3947, 1583424] C777
53) [2969, 1379, 260900] C777 50) [2609, 2758, 858041] C777
54) [3001, 3298, 1746877] C777 130) [14437, 1649, 243081] C777
55) [3109, 2417, 1366425] C777 99) [6073, 4607, 4029264] C777
56) [3209, 3118, 1608977] C777 72) [4457, 1559, 205376] C777
57) [3209, 726, 80425] C777 58) [3217, 363, 12836] C777
58) [3217, 363, 12836] C777 57) [3209, 726, 80425] C777
59) [3217, 1534, 382401] C777 76) [4721, 767, 51472] C777
60) [3221, 6850, 895181] C777 146) [18269, 3425, 2708861] C777
61) [3229, 2457, 152225] C777 ---) [6089, 4583, 1291600] C259
62) [3301, 6405, 2491229] C777 134) [14741, 3841, 2063125] C777
63) [3389, 4538, 2098261] C777 144) [17341, 2269, 762525] C777
64) [3449, 2695, 221456] C777 ---) [13841, 5390, 6377201] C3885
65) [3793, 5386, 7115701] C777 106) [8461, 2693, 34137] C777
66) [3853, 2906, 1356021] C777 ---) [16741, 1453, 188797] C3885
67) [4057, 3611, 1717156] C777 ---) [8761, 5191, 584208] C3 x C6993
68) [4133, 3094, 12601] C777 126) [12601, 1547, 595152] C777
69) [4177, 3035, 371988] C777 ---) [10333, 6070, 7723273] C3 x C777
70) [4177, 3967, 541504] C777 105) [8461, 5389, 5718313] C777
71) [4457, 1063, 272464] C777 143) [17029, 2126, 40113] C777
72) [4457, 1559, 205376] C777 56) [3209, 3118, 1608977] C777
73) [4597, 330, 8837] C777 110) [8837, 165, 4597] C777
74) [4621, 661, 98833] C777 42) [2017, 1322, 41589] C777
75) [4657, 7858, 1857229] C777 ---) [15349, 3929, 3394953] C3 x C777
76) [4721, 767, 51472] C777 59) [3217, 1534, 382401] C777
77) [4933, 5906, 18397] C777 ---) [18397, 2953, 2175453] C259
78) [4933, 369, 3209] C777 ---) [3209, 738, 123325] C259
79) [4937, 1986, 18397] C777 147) [18397, 993, 241913] C777
80) [4957, 2621, 1507977] C777 150) [18617, 5242, 837733] C777
81) [4973, 3053, 2299121] C777 151) [19001, 6106, 124325] C777
82) [5153, 299, 10756] C777 51) [2689, 598, 46377] C777
83) [5189, 6197, 9495625] C777 ---) [15193, 7107, 3507764] C3 x C777
84) [5209, 7803, 2968832] C777 123) [11597, 3997, 1880449] C777
85) [5273, 4486, 1993801] C777 ---) [3769, 2243, 759312] C111
86) [5297, 695, 13492] C777 ---) [3373, 1390, 429057] C259
87) [5333, 7306, 11909] C777 ---) [11909, 3653, 3333125] C259
88) [5333, 1658, 495253] C777 ---) [4093, 829, 47997] C259
89) [5393, 5807, 7134644] C777 133) [14741, 8401, 16313825] C777
90) [5393, 527, 68084] C777 142) [17021, 1054, 5393] C777
91) [5417, 4231, 1971332] C777 ---) [4073, 3343, 2621828] C111
92) [5417, 1423, 17348] C777 ---) [4337, 2846, 1955537] C111
93) [5417, 490, 38357] C777 ---) [317, 245, 5417] C111
94) [5557, 8313, 17108393] C777 ---) [12497, 4179, 88912] C7 x C777
95) [5641, 1811, 705700] C777 ---) [7057, 3622, 456921] C21 x C777
96) [5813, 6118, 1823833] C777 136) [15073, 3059, 1883412] C777
97) [5881, 6271, 5701428] C777 145) [17597, 8269, 5651641] C777
98) [5981, 670, 16529] C777 141) [16529, 335, 23924] C777
99) [6073, 4607, 4029264] C777 55) [3109, 2417, 1366425] C777
100) [7537, 1847, 308304] C777 ---) [2141, 3694, 2178193] C259
101) [7537, 3047, 1143396] C777 ---) [3529, 4891, 5909008] C259
102) [7753, 714, 96437] C777 ---) [797, 357, 7753] C259
103) [8069, 3369, 75925] C777 ---) [3037, 3681, 2912909] C259
104) [8209, 1550, 75249] C777 31) [929, 775, 131344] C777
105) [8461, 5389, 5718313] C777 70) [4177, 3967, 541504] C777
106) [8461, 2693, 34137] C777 65) [3793, 5386, 7115701] C777
107) [8581, 2070, 522041] C777 ---) [3089, 1035, 137296] C259
108) [8597, 4082, 4733] C777 ---) [4733, 2041, 1040237] C259
109) [8597, 1654, 133721] C777 ---) [2729, 827, 137552] C259
110) [8837, 165, 4597] C777 73) [4597, 330, 8837] C777
111) [9257, 2470, 1377113] C777 38) [1433, 1235, 37028] C777
112) [9413, 410, 4373] C777 ---) [4373, 205, 9413] C259
113) [9413, 5961, 691717] C777 ---) [4093, 3849, 2720357] C259
114) [9497, 3115, 1169828] C777 47) [2417, 3823, 607808] C777
115) [9833, 402, 1069] C777 ---) [1069, 201, 9833] C259
116) [10313, 3710, 3276017] C777 ---) [2393, 1855, 41252] C111
117) [10313, 2959, 20612] C777 ---) [5153, 5918, 8673233] C111
118) [10657, 2019, 952484] C777 37) [1409, 3739, 42628] C777
119) [10733, 434, 4157] C777 ---) [4157, 217, 10733] C259
120) [10949, 1981, 365209] C777 ---) [2161, 3962, 2463525] C259
121) [10957, 1505, 563517] C777 ---) [773, 3010, 10957] C111
122) [10993, 3947, 1583424] C777 52) [2749, 4397, 98937] C777
123) [11597, 3997, 1880449] C777 84) [5209, 7803, 2968832] C777
124) [11789, 701, 96325] C777 ---) [3853, 1402, 106101] C259
125) [11789, 145, 2309] C777 ---) [2309, 290, 11789] C259
126) [12601, 1547, 595152] C777 68) [4133, 3094, 12601] C777
127) [13537, 2218, 1175733] C777 ---) [773, 1109, 13537] C259
128) [13577, 3239, 148372] C777 ---) [757, 1713, 665273] C259
129) [14197, 6653, 11062053] C777 ---) [4253, 4677, 695653] C259
130) [14437, 1649, 243081] C777 54) [3001, 3298, 1746877] C777
131) [14653, 2990, 124993] C777 ---) [1033, 1495, 527508] C259
132) [14653, 3485, 2593053] C777 ---) [3557, 6970, 1773013] C259
133) [14741, 8401, 16313825] C777 89) [5393, 5807, 7134644] C777
134) [14741, 3841, 2063125] C777 62) [3301, 6405, 2491229] C777
135) [15061, 4313, 1905625] C777 ---) [3049, 5875, 542196] C259
136) [15073, 3059, 1883412] C777 96) [5813, 6118, 1823833] C777
137) [15277, 2977, 1111869] C777 ---) [1021, 3173, 15277] C111
138) [15973, 4513, 2180713] C777 49) [2593, 6043, 255568] C777
139) [16433, 4187, 1387828] C777 44) [2053, 6045, 5932313] C777
140) [16481, 6150, 5236489] C777 ---) [5449, 3075, 1054784] C259
141) [16529, 335, 23924] C777 98) [5981, 670, 16529] C777
142) [17021, 1054, 5393] C777 90) [5393, 527, 68084] C777
143) [17029, 2126, 40113] C777 71) [4457, 1063, 272464] C777
144) [17341, 2269, 762525] C777 63) [3389, 4538, 2098261] C777
145) [17597, 8269, 5651641] C777 97) [5881, 6271, 5701428] C777
146) [18269, 3425, 2708861] C777 60) [3221, 6850, 895181] C777
147) [18397, 993, 241913] C777 79) [4937, 1986, 18397] C777
148) [18521, 5679, 7502500] C777 ---) [3001, 5695, 6000804] C259
149) [18521, 2182, 4937] C777 ---) [4937, 1091, 296336] C259
150) [18617, 5242, 837733] C777 80) [4957, 2621, 1507977] C777
151) [19001, 6106, 124325] C777 81) [4973, 3053, 2299121] C777
152) [28657, 1231, 27792] C777 ---) [193, 2462, 1404193] C259
153) [40697, 299, 12176] C777 ---) [761, 598, 40697] C3 x C111
154) [41809, 855, 172304] C777 10) [89, 1710, 41809] C777
155) [42533, 1169, 75809] C777 ---) [41, 1123, 170132] C111
156) [43517, 225, 1777] C777 41) [1777, 450, 43517] C777
157) [50593, 2063, 1051344] C777 ---) [149, 2601, 1264825] C259
158) [63629, 1042, 16925] C777 ---) [677, 521, 63629] C259
159) [67733, 1042, 509] C777 ---) [509, 521, 67733] C259
160) [68813, 265, 353] C777 ---) [353, 530, 68813] C259
161) [116993, 351, 1552] C777 12) [97, 702, 116993] C777
162) [129953, 391, 5732] C777 ---) [1433, 782, 129953] C259
163) [144253, 649, 69237] C777 ---) [157, 1298, 144253] C111
164) [180497, 1047, 228928] C777 8) [73, 2094, 180497] C777
165) [185441, 687, 71632] C777 ---) [37, 1374, 185441] C259
166) [203381, 453, 457] C777 23) [457, 906, 203381] C777
167) [211217, 503, 10448] C777 27) [653, 1006, 211217] C777
168) [228457, 755, 85392] C777 ---) [593, 1510, 228457] C259
169) [258581, 2186, 160325] C777 ---) [53, 1093, 258581] C259
170) [260549, 757, 78125] C777 ---) [5, 1021, 260549] C37
171) [292517, 541, 41] C777 ---) [41, 1082, 292517] C259
172) [346133, 2378, 29189] C777 ---) [101, 1189, 346133] C259
173) [385493, 2498, 18029] C777 ---) [149, 1249, 385493] C259
174) [400313, 643, 3284] C777 30) [821, 1286, 400313] C777
175) [405749, 2586, 48853] C777 32) [997, 1293, 405749] C777
176) [457201, 1063, 168192] C777 9) [73, 2126, 457201] C777
177) [522569, 1763, 646400] C777 ---) [101, 3526, 522569] C259
178) [547817, 979, 102656] C777 ---) [401, 1958, 547817] C1295
179) [556849, 757, 4050] C777 ---) [8, 1514, 556849] C259
180) [615289, 1163, 184320] C777 ---) [5, 1569, 615289] C111
181) [726337, 863, 4608] C777 ---) [8, 1726, 726337] C259
182) [733561, 931, 33300] C777 ---) [37, 1862, 733561] C259
183) [757381, 3482, 1557] C777 14) [173, 1741, 757381] C777
184) [777433, 1307, 232704] C777 13) [101, 2614, 777433] C777
185) [821449, 1027, 58320] C777 ---) [5, 2001, 821449] C111
186) [922169, 1163, 107600] C777 22) [269, 2326, 922169] C777
187) [1035953, 1095, 40768] C777 ---) [13, 2190, 1035953] C259
188) [1082381, 1041, 325] C777 ---) [13, 2082, 1082381] C259
189) [1105193, 1075, 12608] C777 15) [197, 2150, 1105193] C777
190) [1248413, 1121, 2057] C777 ---) [17, 2242, 1248413] C259
191) [1250201, 3503, 254800] C777 ---) [13, 3129, 1250201] C259
192) [2243809, 1999, 438048] C777 2) [8, 3998, 2243809] C777
193) [2613761, 1631, 11600] C777 7) [29, 3262, 2613761] C777
194) [2663081, 1651, 15680] C777 ---) [5, 3302, 2663081] C259
195) [2798329, 1739, 56448] C777 ---) [8, 3478, 2798329] C259
196) [2965849, 2011, 269568] C777 ---) [13, 4022, 2965849] C259
197) [3052297, 1763, 13968] C777 11) [97, 3526, 3052297] C777
198) [3273449, 1811, 1568] C777 ---) [8, 3622, 3273449] C259
199) [3869417, 2131, 167936] C777 ---) [41, 4262, 3869417] C259
200) [3916169, 1987, 8000] C777 ---) [5, 3974, 3916169] C259
201) [4683817, 2195, 33552] C777 19) [233, 4390, 4683817] C777
202) [5641369, 2587, 262800] C777 ---) [73, 5174, 5641369] C259
203) [6386209, 2767, 317520] C777 ---) [5, 5534, 6386209] C259
204) [7746569, 2787, 5200] C777 5) [13, 5574, 7746569] C777
205) [12435977, 3587, 107648] C777 ---) [8, 7174, 12435977] C259