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 C789 non-normal (D4) quartic CM field invariants: 185 fields

K Quartic invariants Cl(OK) Igusa invariants Kr Reflex invariants Cl(OKr) Igusa invariants
1) [8, 4750, 5392817] C789 179) [5392817, 2375, 61952] C789
2) [8, 5182, 6711233] C789 ---) [6711233, 2591, 512] C3 x C11835
3) [8, 5902, 8695601] C789 182) [8695601, 2951, 3200] C789
4) [13, 6750, 11289953] C789 183) [11289953, 3375, 25168] C789
5) [13, 8457, 16775573] C789 185) [16775573, 12905, 3889717] C789
6) [29, 3958, 3018137] C789 175) [3018137, 1979, 224576] C789
7) [29, 5534, 7470689] C789 181) [7470689, 2767, 46400] C789
8) [37, 4926, 5829569] C789 ---) [5829569, 2463, 59200] C3 x C2367
9) [41, 1286, 412793] C789 154) [412793, 643, 164] C789
10) [41, 1486, 384113] C789 ---) [384113, 743, 41984] C3 x C789
11) [41, 1934, 869489] C789 165) [869489, 967, 16400] C789
12) [73, 5422, 7330833] C789 162) [814537, 2711, 4672] C789
13) [73, 3406, 1704177] C789 150) [189353, 1703, 299008] C789
14) [101, 2902, 2001977] C789 172) [2001977, 1451, 25856] C789
15) [101, 3142, 1685897] C789 170) [1685897, 1571, 195536] C789
16) [173, 1870, 774577] C789 161) [774577, 935, 24912] C789
17) [173, 3398, 1015433] C789 ---) [1015433, 1699, 467792] C14991
18) [229, 285, 20249] C789 135) [20249, 570, 229] C789
19) [229, 405, 40949] C789 ---) [40949, 810, 229] C263
20) [233, 766, 87041] C789 ---) [87041, 383, 14912] C3 x C789
21) [257, 2998, 602201] C789 ---) [602201, 1499, 411200] C3419
22) [293, 2030, 955217] C789 166) [955217, 1015, 18752] C789
23) [317, 1910, 830873] C789 163) [830873, 955, 20288] C789
24) [337, 3318, 2730713] C789 174) [2730713, 1659, 5392] C789
25) [569, 850, 178349] C789 149) [178349, 425, 569] C789
26) [617, 2398, 16033] C789 122) [16033, 1199, 355392] C789
27) [653, 997, 176509] C789 148) [176509, 1994, 287973] C789
28) [661, 1014, 87833] C789 143) [87833, 507, 42304] C789
29) [673, 594, 85517] C789 ---) [85517, 297, 673] C3 x C789
30) [677, 1469, 531197] C789 157) [531197, 2938, 33173] C789
31) [677, 1441, 517597] C789 156) [517597, 2882, 6093] C789
32) [709, 2713, 1481161] C789 113) [12241, 1663, 2836] C789
33) [809, 1126, 304025] C789 ---) [12161, 563, 3236] C8679
34) [1013, 862, 169553] C789 146) [169553, 431, 4052] C789
35) [1193, 1923, 22276] C789 84) [5569, 1803, 577412] C789
36) [1433, 1531, 41092] C789 ---) [10273, 3062, 2179593] C3 x C2367
37) [1489, 771, 85700] C789 ---) [857, 831, 95296] C263
38) [1861, 590, 57249] C789 92) [6361, 295, 7444] C789
39) [1973, 1757, 771269] C789 160) [771269, 3514, 1973] C789
40) [2017, 830, 43137] C789 74) [4793, 415, 32272] C789
41) [2113, 3971, 1570896] C789 ---) [10909, 3001, 2030593] C3945
42) [2377, 4678, 869049] C789 106) [10729, 2339, 1150468] C789
43) [2381, 6357, 802081] C789 ---) [16369, 4151, 2142900] C3 x C789
44) [2557, 3762, 3036989] C789 86) [5741, 1881, 125293] C789
45) [2677, 2358, 1218713] C789 ---) [4217, 1179, 42832] C263
46) [2729, 2015, 517696] C789 97) [8089, 4030, 1989441] C789
47) [2729, 2007, 73012] C789 ---) [18253, 4014, 3736001] C3945
48) [2729, 1187, 198736] C789 114) [12421, 2374, 614025] C789
49) [2801, 1982, 265025] C789 105) [10601, 991, 179264] C789
50) [2857, 4579, 5081104] C789 ---) [6481, 2987, 1645632] C1315
51) [2857, 2875, 980032] C789 ---) [15313, 5750, 4345497] C263
52) [2909, 4098, 835597] C789 ---) [17053, 2049, 840701] C3 x C789
53) [2917, 2669, 29961] C789 ---) [3329, 2919, 291700] C263
54) [3037, 3289, 2642881] C789 94) [7321, 3431, 437328] C789
55) [3041, 1431, 474688] C789 95) [7417, 2862, 149009] C789
56) [3209, 4415, 3389696] C789 117) [13241, 4823, 1283600] C789
57) [3361, 5347, 4222692] C789 ---) [13033, 4231, 483984] C10257
58) [3373, 473, 55089] C789 91) [6121, 946, 3373] C789
59) [3449, 2699, 1778900] C789 129) [17789, 5398, 169001] C789
60) [3697, 650, 90837] C789 104) [10093, 325, 3697] C789
61) [3701, 5177, 15401] C789 120) [15401, 7523, 2501876] C789
62) [3761, 4318, 810017] C789 75) [4793, 2159, 962816] C789
63) [3761, 5379, 3960400] C789 101) [9901, 6117, 6322241] C789
64) [4021, 3361, 209425] C789 99) [8377, 5011, 5806324] C789
65) [4049, 7367, 6926800] C789 126) [17317, 4773, 3405209] C789
66) [4073, 802, 14173] C789 118) [14173, 401, 36657] C789
67) [4153, 4843, 4733008] C789 90) [6037, 3745, 3492673] C789
68) [4177, 3322, 1405573] C789 98) [8317, 1661, 338337] C789
69) [4241, 2851, 1649300] C789 125) [16493, 5702, 1531001] C789
70) [4261, 5486, 4183425] C789 133) [18593, 2743, 835156] C789
71) [4421, 1306, 408725] C789 124) [16349, 653, 4421] C789
72) [4549, 1473, 404825] C789 123) [16193, 2946, 550429] C789
73) [4789, 3121, 10729] C789 107) [10729, 6242, 9697725] C789
74) [4793, 415, 32272] C789 40) [2017, 830, 43137] C789
75) [4793, 2159, 962816] C789 62) [3761, 4318, 810017] C789
76) [4861, 3030, 2217449] C789 116) [13121, 1515, 19444] C789
77) [4909, 2681, 1147725] C789 79) [5101, 4709, 1104525] C789
78) [5081, 1375, 14096] C789 ---) [881, 2123, 508100] C263
79) [5101, 4709, 1104525] C789 77) [4909, 2681, 1147725] C789
80) [5189, 5654, 3923753] C789 ---) [13577, 2827, 1017044] C3 x C789
81) [5209, 330, 6389] C789 93) [6389, 165, 5209] C789
82) [5261, 7597, 14206325] C789 ---) [11597, 4093, 636581] C263
83) [5333, 3437, 8093] C789 ---) [8093, 6281, 9860717] C263
84) [5569, 1803, 577412] C789 35) [1193, 1923, 22276] C789
85) [5669, 5201, 15073] C789 119) [15073, 8243, 16530804] C789
86) [5741, 1881, 125293] C789 44) [2557, 3762, 3036989] C789
87) [5813, 3046, 2226521] C789 131) [18401, 1523, 23252] C789
88) [5821, 6294, 590009] C789 ---) [12041, 3147, 2328400] C1315
89) [5849, 4114, 277325] C789 109) [11093, 2057, 988481] C789
90) [6037, 3745, 3492673] C789 67) [4153, 4843, 4733008] C789
91) [6121, 946, 3373] C789 58) [3373, 473, 55089] C789
92) [6361, 295, 7444] C789 38) [1861, 590, 57249] C789
93) [6389, 165, 5209] C789 81) [5209, 330, 6389] C789
94) [7321, 3431, 437328] C789 54) [3037, 3289, 2642881] C789
95) [7417, 2862, 149009] C789 55) [3041, 1431, 474688] C789
96) [8069, 1306, 135925] C789 ---) [5437, 653, 72621] C263
97) [8089, 4030, 1989441] C789 46) [2729, 2015, 517696] C789
98) [8317, 1661, 338337] C789 68) [4177, 3322, 1405573] C789
99) [8377, 5011, 5806324] C789 64) [4021, 3361, 209425] C789
100) [9133, 2490, 1513493] C789 ---) [5237, 1245, 9133] C263
101) [9901, 6117, 6322241] C789 63) [3761, 5379, 3960400] C789
102) [10069, 4174, 327969] C789 ---) [4049, 2087, 1006900] C263
103) [10069, 4865, 2470941] C789 ---) [2269, 3353, 2265525] C263
104) [10093, 325, 3697] C789 60) [3697, 650, 90837] C789
105) [10601, 991, 179264] C789 49) [2801, 1982, 265025] C789
106) [10729, 2339, 1150468] C789 42) [2377, 4678, 869049] C789
107) [10729, 6242, 9697725] C789 73) [4789, 3121, 10729] C789
108) [10949, 4217, 698477] C789 ---) [4133, 5369, 5792021] C263
109) [11093, 2057, 988481] C789 89) [5849, 4114, 277325] C789
110) [11789, 769, 144893] C789 ---) [2957, 1538, 11789] C263
111) [12197, 1545, 81433] C789 ---) [673, 2687, 1756368] C263
112) [12197, 5869, 6705509] C789 ---) [3989, 4741, 304925] C263
113) [12241, 1663, 2836] C789 32) [709, 2713, 1481161] C789
114) [12421, 2374, 614025] C789 48) [2729, 1187, 198736] C789
115) [12821, 2466, 238189] C789 ---) [4861, 1233, 320525] C263
116) [13121, 1515, 19444] C789 76) [4861, 3030, 2217449] C789
117) [13241, 4823, 1283600] C789 56) [3209, 4415, 3389696] C789
118) [14173, 401, 36657] C789 66) [4073, 802, 14173] C789
119) [15073, 8243, 16530804] C789 85) [5669, 5201, 15073] C789
120) [15401, 7523, 2501876] C789 61) [3701, 5177, 15401] C789
121) [15881, 1186, 288125] C789 ---) [461, 593, 15881] C263
122) [16033, 1199, 355392] C789 26) [617, 2398, 16033] C789
123) [16193, 2946, 550429] C789 72) [4549, 1473, 404825] C789
124) [16349, 653, 4421] C789 71) [4421, 1306, 408725] C789
125) [16493, 5702, 1531001] C789 69) [4241, 2851, 1649300] C789
126) [17317, 4773, 3405209] C789 65) [4049, 7367, 6926800] C789
127) [17477, 141, 601] C789 ---) [601, 282, 17477] C263
128) [17609, 5302, 5900825] C789 ---) [4817, 2651, 281744] C263
129) [17789, 5398, 169001] C789 59) [3449, 2699, 1778900] C789
130) [18257, 1771, 12752] C789 ---) [797, 3542, 3085433] C263
131) [18401, 1523, 23252] C789 87) [5813, 3046, 2226521] C789
132) [18541, 3650, 3256461] C789 ---) [2141, 1825, 18541] C263
133) [18593, 2743, 835156] C789 70) [4261, 5486, 4183425] C789
134) [19469, 709, 3989] C789 ---) [3989, 1418, 486725] C263
135) [20249, 570, 229] C789 18) [229, 285, 20249] C789
136) [22397, 417, 37873] C789 ---) [313, 834, 22397] C263
137) [26113, 674, 9117] C789 ---) [1013, 337, 26113] C263
138) [27409, 1810, 709389] C789 ---) [149, 905, 27409] C263
139) [33521, 263, 8912] C789 ---) [557, 526, 33521] C263
140) [34157, 209, 2381] C789 ---) [2381, 418, 34157] C263
141) [65981, 409, 25325] C789 ---) [1013, 818, 65981] C263
142) [68669, 265, 389] C789 ---) [389, 530, 68669] C263
143) [87833, 507, 42304] C789 28) [661, 1014, 87833] C789
144) [94397, 1282, 33293] C789 ---) [197, 641, 94397] C263
145) [127481, 707, 93092] C789 ---) [17, 1414, 127481] C263
146) [169553, 431, 4052] C789 34) [1013, 862, 169553] C789
147) [174653, 561, 35017] C789 ---) [97, 1122, 174653] C263
148) [176509, 1994, 287973] C789 27) [653, 997, 176509] C789
149) [178349, 425, 569] C789 25) [569, 850, 178349] C789
150) [189353, 1703, 299008] C789 13) [73, 3406, 1704177] C789
151) [273929, 771, 80128] C789 ---) [313, 1542, 273929] C263
152) [284057, 539, 1616] C789 ---) [101, 1078, 284057] C263
153) [291077, 541, 401] C789 ---) [401, 1082, 291077] C3945
154) [412793, 643, 164] C789 9) [41, 1286, 412793] C789
155) [456529, 677, 450] C789 ---) [8, 1354, 456529] C263
156) [517597, 2882, 6093] C789 31) [677, 1441, 517597] C789
157) [531197, 2938, 33173] C789 30) [677, 1469, 531197] C789
158) [669049, 1291, 249408] C789 ---) [433, 2582, 669049] C263
159) [752489, 1683, 520000] C789 ---) [13, 2913, 752489] C263
160) [771269, 3514, 1973] C789 39) [1973, 1757, 771269] C789
161) [774577, 935, 24912] C789 16) [173, 1870, 774577] C789
162) [814537, 2711, 4672] C789 12) [73, 5422, 7330833] C789
163) [830873, 955, 20288] C789 23) [317, 1910, 830873] C789
164) [833537, 1023, 53248] C789 ---) [13, 2046, 833537] C263
165) [869489, 967, 16400] C789 11) [41, 1934, 869489] C789
166) [955217, 1015, 18752] C789 22) [293, 2030, 955217] C789
167) [1117169, 1063, 3200] C789 ---) [8, 2126, 1117169] C263
168) [1391861, 1181, 725] C789 ---) [29, 2362, 1391861] C263
169) [1509133, 1249, 12717] C789 ---) [157, 2498, 1509133] C263
170) [1685897, 1571, 195536] C789 15) [101, 3142, 1685897] C789
171) [1932001, 1391, 720] C789 ---) [5, 2782, 1932001] C263
172) [2001977, 1451, 25856] C789 14) [101, 2902, 2001977] C789
173) [2534953, 4967, 464128] C789 ---) [37, 9565, 22814577] C263
174) [2730713, 1659, 5392] C789 24) [337, 3318, 2730713] C789
175) [3018137, 1979, 224576] C789 6) [29, 3958, 3018137] C789
176) [3288889, 1963, 141120] C789 ---) [5, 3926, 3288889] C263
177) [3455033, 1889, 28322] C789 ---) [8, 3778, 3455033] C263
178) [4434329, 2107, 1280] C789 ---) [5, 4214, 4434329] C263
179) [5392817, 2375, 61952] C789 1) [8, 4750, 5392817] C789
180) [6054089, 2467, 8000] C789 ---) [5, 4934, 6054089] C263
181) [7470689, 2767, 46400] C789 7) [29, 5534, 7470689] C789
182) [8695601, 2951, 3200] C789 3) [8, 5902, 8695601] C789
183) [11289953, 3375, 25168] C789 4) [13, 6750, 11289953] C789
184) [12210449, 3607, 200000] C789 ---) [5, 7214, 12210449] C263
185) [16775573, 12905, 3889717] C789 5) [13, 8457, 16775573] C789