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 number 771 non-normal (D4) quartic CM field invariants: 161 fields

K Quartic invariants Cl(OK) Igusa invariants Kr Reflex invariants Cl(OKr) Igusa invariants
1) [8, 4462, 3748049] C771 154) [3748049, 2231, 307328] C771
2) [8, 4526, 4788241] C771 155) [4788241, 2263, 83232] C771
3) [8, 5422, 7144721] C771 159) [7144721, 2711, 51200] C771
4) [13, 9926, 24584569] C771 161) [24584569, 4963, 11700] C771
5) [53, 3334, 2290441] C771 ---) [2290441, 1667, 122112] C3 x C771
6) [53, 3646, 2658497] C771 ---) [2658497, 1823, 166208] C8481
7) [53, 4454, 4945961] C771 157) [4945961, 2227, 3392] C771
8) [53, 4486, 4813961] C771 156) [4813961, 2243, 54272] C771
9) [53, 2806, 1846297] C771 148) [1846297, 1403, 30528] C771
10) [73, 2478, 184913] C771 128) [184913, 1239, 337552] C771
11) [113, 6022, 9001033] C771 ---) [9001033, 3011, 16272] C3 x C771
12) [149, 3958, 2304857] C771 151) [2304857, 1979, 402896] C771
13) [157, 1758, 732449] C771 138) [732449, 879, 10048] C771
14) [173, 2246, 1216841] C771 143) [1216841, 1123, 11072] C771
15) [241, 2446, 1434033] C771 127) [159337, 1223, 15424] C771
16) [241, 750, 125201] C771 ---) [125201, 375, 3856] C10023
17) [269, 1358, 456737] C771 ---) [456737, 679, 1076] C3855
18) [293, 1486, 547361] C771 133) [547361, 743, 1172] C771
19) [373, 1998, 401201] C771 ---) [401201, 999, 149200] C5397
20) [421, 798, 132257] C771 126) [132257, 399, 6736] C771
21) [433, 3039, 277136] C771 110) [17321, 1719, 6928] C771
22) [557, 1146, 326101] C771 130) [326101, 573, 557] C771
23) [673, 2007, 158864] C771 86) [9929, 1687, 689152] C771
24) [769, 670, 63009] C771 79) [7001, 335, 12304] C771
25) [797, 1333, 372293] C771 ---) [372293, 2666, 287717] C5397
26) [1097, 499, 40036] C771 87) [10009, 998, 88857] C771
27) [1217, 778, 107509] C771 124) [107509, 389, 10953] C771
28) [1433, 1034, 261557] C771 ---) [261557, 517, 1433] C3 x C771
29) [1433, 3263, 193808] C771 93) [12113, 4075, 5732] C771
30) [1669, 582, 57977] C771 121) [57977, 291, 6676] C771
31) [1873, 702, 3329] C771 44) [3329, 351, 29968] C771
32) [2017, 1239, 68624] C771 50) [4289, 2478, 1260625] C771
33) [2269, 5757, 4922537] C771 ---) [17033, 3543, 2622964] C3855
34) [2269, 4333, 1502941] C771 94) [12421, 5365, 3814189] C771
35) [2293, 2537, 1539729] C771 115) [19009, 5074, 277453] C771
36) [2521, 4298, 1703925] C771 ---) [7573, 2149, 728569] C3 x C2313
37) [2549, 2965, 2197169] C771 97) [13001, 5930, 2549] C771
38) [2617, 635, 47812] C771 92) [11953, 1270, 211977] C771
39) [2621, 4005, 2169409] C771 ---) [17929, 6111, 1048400] C3 x C771
40) [2689, 1195, 243396] C771 78) [6761, 2390, 454441] C771
41) [2749, 4013, 940977] C771 91) [11617, 5747, 98964] C771
42) [2777, 2619, 1047616] C771 107) [16369, 5238, 2668697] C771
43) [2801, 1603, 636100] C771 77) [6361, 3206, 25209] C771
44) [3329, 351, 29968] C771 31) [1873, 702, 3329] C771
45) [3557, 1697, 612353] C771 ---) [12497, 3394, 430397] C5397
46) [4021, 2926, 1883025] C771 81) [8369, 1463, 64336] C771
47) [4093, 6146, 782541] C771 84) [9661, 3073, 2165197] C771
48) [4129, 5482, 229525] C771 ---) [9181, 2741, 1820889] C3855
49) [4241, 7746, 6026173] C771 109) [16693, 3873, 2243489] C771
50) [4289, 2478, 1260625] C771 32) [2017, 1239, 68624] C771
51) [4481, 4234, 448789] C771 ---) [3709, 2117, 1008225] C257
52) [4513, 579, 55604] C771 99) [13901, 1158, 112825] C771
53) [4649, 2698, 313525] C771 ---) [12541, 1349, 376569] C257
54) [4729, 3398, 2205625] C771 ---) [3529, 1699, 170244] C257
55) [4733, 5305, 6977777] C771 80) [8297, 4447, 3199508] C771
56) [4801, 5455, 7342036] C771 89) [10861, 4789, 235249] C771
57) [4937, 4658, 3034733] C771 ---) [17957, 2329, 597377] C5397
58) [5009, 1963, 50452] C771 95) [12613, 3926, 3651561] C771
59) [5021, 273, 17377] C771 111) [17377, 546, 5021] C771
60) [5101, 6465, 3653249] C771 96) [12641, 6415, 20404] C771
61) [5101, 3502, 127825] C771 62) [5113, 1751, 734544] C771
62) [5113, 1751, 734544] C771 61) [5101, 3502, 127825] C771
63) [5501, 2837, 1405657] C771 90) [11617, 5674, 2425941] C771
64) [5569, 6799, 11243344] C771 100) [14341, 5885, 50121] C771
65) [5573, 3486, 2948881] C771 113) [17449, 1743, 22292] C771
66) [5581, 785, 85689] C771 83) [9521, 1570, 273469] C771
67) [5581, 6886, 8639593] C771 ---) [10273, 3443, 803664] C3 x C2313
68) [5657, 2855, 101648] C771 76) [6353, 5710, 7744433] C771
69) [5669, 7233, 8145625] C771 ---) [13033, 5231, 816336] C10023
70) [5669, 7389, 314425] C771 ---) [12577, 6859, 816336] C3 x C771
71) [5741, 569, 10613] C771 ---) [10613, 1138, 281309] C1285
72) [5813, 337, 15313] C771 104) [15313, 674, 52317] C771
73) [5849, 9090, 16703101] C771 116) [19861, 4545, 988481] C771
74) [5881, 5523, 214352] C771 98) [13397, 7217, 12991129] C771
75) [6053, 549, 1201] C771 ---) [1201, 1098, 296597] C257
76) [6353, 5710, 7744433] C771 68) [5657, 2855, 101648] C771
77) [6361, 3206, 25209] C771 43) [2801, 1603, 636100] C771
78) [6761, 2390, 454441] C771 40) [2689, 1195, 243396] C771
79) [7001, 335, 12304] C771 24) [769, 670, 63009] C771
80) [8297, 4447, 3199508] C771 55) [4733, 5305, 6977777] C771
81) [8369, 1463, 64336] C771 46) [4021, 2926, 1883025] C771
82) [8837, 2733, 486541] C771 ---) [4021, 5466, 5523125] C257
83) [9521, 1570, 273469] C771 66) [5581, 785, 85689] C771
84) [9661, 3073, 2165197] C771 47) [4093, 6146, 782541] C771
85) [9749, 894, 43825] C771 ---) [1753, 447, 38996] C257
86) [9929, 1687, 689152] C771 23) [673, 2007, 158864] C771
87) [10009, 998, 88857] C771 26) [1097, 499, 40036] C771
88) [10301, 4346, 4680725] C771 ---) [3821, 2173, 10301] C257
89) [10861, 4789, 235249] C771 56) [4801, 5455, 7342036] C771
90) [11617, 5674, 2425941] C771 63) [5501, 2837, 1405657] C771
91) [11617, 5747, 98964] C771 41) [2749, 4013, 940977] C771
92) [11953, 1270, 211977] C771 38) [2617, 635, 47812] C771
93) [12113, 4075, 5732] C771 29) [1433, 3263, 193808] C771
94) [12421, 5365, 3814189] C771 34) [2269, 4333, 1502941] C771
95) [12613, 3926, 3651561] C771 58) [5009, 1963, 50452] C771
96) [12641, 6415, 20404] C771 60) [5101, 6465, 3653249] C771
97) [13001, 5930, 2549] C771 37) [2549, 2965, 2197169] C771
98) [13397, 7217, 12991129] C771 74) [5881, 5523, 214352] C771
99) [13901, 1158, 112825] C771 52) [4513, 579, 55604] C771
100) [14341, 5885, 50121] C771 64) [5569, 6799, 11243344] C771
101) [14389, 2765, 8361] C771 ---) [929, 2483, 1438900] C257
102) [14389, 5621, 7607533] C771 ---) [5557, 8297, 5194429] C257
103) [15193, 4807, 1123956] C771 ---) [3469, 6349, 1230633] C257
104) [15313, 674, 52317] C771 72) [5813, 337, 15313] C771
105) [15641, 711, 28624] C771 ---) [1789, 1422, 391025] C257
106) [16369, 4534, 948825] C771 ---) [4217, 2267, 1047616] C257
107) [16369, 5238, 2668697] C771 42) [2777, 2619, 1047616] C771
108) [16673, 1323, 333376] C771 ---) [5209, 2646, 416825] C257
109) [16693, 3873, 2243489] C771 49) [4241, 7746, 6026173] C771
110) [17321, 1719, 6928] C771 21) [433, 3039, 277136] C771
111) [17377, 546, 5021] C771 59) [5021, 273, 17377] C771
112) [17417, 1199, 320212] C771 ---) [277, 2398, 156753] C257
113) [17449, 1743, 22292] C771 65) [5573, 3486, 2948881] C771
114) [18521, 5790, 8084689] C771 ---) [1801, 2895, 74084] C257
115) [19009, 5074, 277453] C771 35) [2293, 2537, 1539729] C771
116) [19861, 4545, 988481] C771 73) [5849, 9090, 16703101] C771
117) [20249, 655, 61696] C771 ---) [241, 1310, 182241] C257
118) [24749, 533, 15337] C771 ---) [313, 1066, 222741] C257
119) [25717, 1978, 52309] C771 ---) [181, 989, 231453] C257
120) [35317, 770, 6957] C771 ---) [773, 385, 35317] C257
121) [57977, 291, 6676] C771 30) [1669, 582, 57977] C771
122) [68813, 769, 130637] C771 ---) [773, 1538, 68813] C257
123) [97241, 1915, 892496] C771 ---) [461, 3830, 97241] C257
124) [107509, 389, 10953] C771 27) [1217, 778, 107509] C771
125) [131489, 1235, 85456] C771 ---) [109, 2470, 1183401] C257
126) [132257, 399, 6736] C771 20) [421, 798, 132257] C771
127) [159337, 1223, 15424] C771 15) [241, 2446, 1434033] C771
128) [184913, 1239, 337552] C771 10) [73, 2478, 184913] C771
129) [301349, 557, 2225] C771 ---) [89, 1114, 301349] C257
130) [326101, 573, 557] C771 22) [557, 1146, 326101] C771
131) [402817, 765, 45602] C771 ---) [8, 1530, 402817] C257
132) [465373, 865, 70713] C771 ---) [97, 1730, 465373] C257
133) [547361, 743, 1172] C771 18) [293, 1486, 547361] C771
134) [603457, 797, 7938] C771 ---) [8, 1594, 603457] C257
135) [662177, 1167, 174928] C771 ---) [13, 2334, 662177] C257
136) [700633, 883, 19764] C771 ---) [61, 1766, 700633] C257
137) [708857, 1579, 446096] C771 ---) [569, 3158, 708857] C257
138) [732449, 879, 10048] C771 13) [157, 1758, 732449] C771
139) [751841, 879, 5200] C771 ---) [13, 1758, 751841] C257
140) [906197, 1053, 50653] C771 ---) [37, 2106, 906197] C257
141) [996161, 3011, 25168] C771 ---) [13, 2469, 996161] C257
142) [1016881, 1031, 11520] C771 ---) [5, 2062, 1016881] C257
143) [1216841, 1123, 11072] C771 14) [173, 2246, 1216841] C771
144) [1229381, 1141, 18125] C771 ---) [29, 2282, 1229381] C257
145) [1252897, 1327, 127008] C771 ---) [8, 2654, 1252897] C257
146) [1256573, 1121, 17] C771 ---) [17, 2242, 1256573] C257
147) [1716041, 1339, 19220] C771 ---) [5, 2678, 1716041] C257
148) [1846297, 1403, 30528] C771 9) [53, 2806, 1846297] C771
149) [2096597, 1469, 15341] C771 ---) [29, 2938, 2096597] C257
150) [2221129, 1603, 87120] C771 ---) [5, 3206, 2221129] C257
151) [2304857, 1979, 402896] C771 12) [149, 3958, 2304857] C771
152) [3216121, 1867, 67392] C771 ---) [13, 3734, 3216121] C257
153) [3493961, 1891, 20480] C771 ---) [5, 3782, 3493961] C257
154) [3748049, 2231, 307328] C771 1) [8, 4462, 3748049] C771
155) [4788241, 2263, 83232] C771 2) [8, 4526, 4788241] C771
156) [4813961, 2243, 54272] C771 8) [53, 4486, 4813961] C771
157) [4945961, 2227, 3392] C771 7) [53, 4454, 4945961] C771
158) [6112681, 2515, 53136] C771 ---) [41, 5030, 6112681] C257
159) [7144721, 2711, 51200] C771 3) [8, 5422, 7144721] C771
160) [8442521, 3611, 1149200] C771 ---) [17, 7222, 8442521] C257
161) [24584569, 4963, 11700] C771 4) [13, 9926, 24584569] C771