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 C737 non-normal (D4) quartic CM field invariants: 189 fields

K Quartic invariants Cl(OK) Igusa invariants Kr Reflex invariants Cl(OKr) Igusa invariants
1) [5, 9238, 21333881] C737 185) [21333881, 4619, 320] C737
2) [5, 12022, 34234841] C737 189) [34234841, 6011, 474320] C737
3) [5, 9526, 18953689] C737 184) [18953689, 4763, 933120] C737
4) [5, 11374, 32295889] C737 ---) [32295889, 5687, 11520] C2211
5) [5, 8806, 17286889] C737 182) [17286889, 4403, 524880] C737
6) [5, 11326, 31997569] C737 188) [31997569, 5663, 18000] C737
7) [5, 8782, 16630961] C737 ---) [16630961, 4391, 662480] C3685
8) [5, 10174, 23285569] C737 186) [23285569, 5087, 648000] C737
9) [5, 7742, 12672641] C737 180) [12672641, 3871, 578000] C737
10) [5, 10462, 25315361] C737 ---) [25315361, 5231, 512000] C6633
11) [5, 6838, 11617561] C737 179) [11617561, 3419, 18000] C737
12) [8, 4366, 2952881] C737 171) [2952881, 2183, 453152] C737
13) [8, 4574, 4327201] C737 172) [4327201, 2287, 225792] C737
14) [8, 7694, 11186737] C737 ---) [11186737, 3847, 903168] C11 x C737
15) [8, 8590, 18346673] C737 183) [18346673, 4295, 25088] C737
16) [8, 12214, 37138649] C737 ---) [37138649, 6107, 39200] C6633
17) [8, 4558, 4374641] C737 173) [4374641, 2279, 204800] C737
18) [13, 5286, 5224937] C737 174) [5224937, 2643, 440128] C737
19) [13, 5814, 7119449] C737 178) [7119449, 2907, 332800] C737
20) [13, 5041, 2326921] C737 170) [2326921, 3011, 1684800] C737
21) [17, 2126, 1076657] C737 163) [1076657, 1063, 13328] C737
22) [17, 10582, 27906553] C737 187) [27906553, 5291, 22032] C737
23) [17, 2110, 1059713] C737 161) [1059713, 1055, 13328] C737
24) [29, 3758, 1509457] C737 167) [1509457, 1879, 505296] C737
25) [37, 3582, 1351169] C737 165) [1351169, 1791, 464128] C737
26) [37, 5054, 5618497] C737 176) [5618497, 2527, 191808] C737
27) [37, 8558, 11404753] C737 ---) [11404753, 4279, 1726272] C3685
28) [41, 2338, 1329661] C737 ---) [1329661, 1169, 9225] C2211
29) [41, 2491, 1341668] C737 151) [335417, 2903, 10496] C737
30) [53, 3478, 1667321] C737 168) [1667321, 1739, 339200] C737
31) [73, 1278, 109313] C737 141) [109313, 639, 74752] C737
32) [73, 2562, 1458461] C737 166) [1458461, 1281, 45625] C737
33) [73, 2106, 1101509] C737 164) [1101509, 1053, 1825] C737
34) [73, 702, 104513] C737 140) [104513, 351, 4672] C737
35) [73, 2082, 1076381] C737 162) [1076381, 1041, 1825] C737
36) [73, 1662, 223361] C737 ---) [223361, 831, 116800] C2211
37) [89, 8342, 14640377] C737 181) [14640377, 4171, 689216] C737
38) [89, 5974, 8831033] C737 ---) [8831033, 2987, 22784] C30217
39) [101, 10046, 22897025] C737 ---) [915881, 5023, 583376] C2211
40) [101, 3862, 2073977] C737 ---) [2073977, 1931, 413696] C2211
41) [109, 2846, 2009233] C737 ---) [2009233, 1423, 3924] C9581
42) [113, 5366, 6475289] C737 177) [6475289, 2683, 180800] C737
43) [137, 1234, 375757] C737 ---) [375757, 617, 1233] C3685
44) [157, 1698, 539309] C737 157) [539309, 849, 45373] C737
45) [173, 1718, 735113] C737 159) [735113, 859, 692] C737
46) [197, 3830, 439577] C737 153) [439577, 1915, 806912] C737
47) [277, 8302, 16947153] C737 169) [1883017, 4151, 70912] C737
48) [277, 3958, 1771353] C737 148) [196817, 1979, 536272] C737
49) [293, 1366, 461801] C737 155) [461801, 683, 1172] C737
50) [317, 4990, 361793] C737 152) [361793, 2495, 1465808] C737
51) [397, 5638, 7845129] C737 160) [871681, 2819, 25408] C737
52) [409, 6038, 5345017] C737 175) [5345017, 3019, 942336] C737
53) [449, 674, 111773] C737 143) [111773, 337, 449] C737
54) [457, 882, 148781] C737 145) [148781, 441, 11425] C737
55) [461, 5326, 6029425] C737 ---) [241177, 2663, 265536] C14003
56) [569, 610, 90749] C737 137) [90749, 305, 569] C737
57) [757, 1026, 187469] C737 147) [187469, 513, 18925] C737
58) [757, 798, 110753] C737 142) [110753, 399, 12112] C737
59) [821, 758, 91097] C737 138) [91097, 379, 13136] C737
60) [877, 1482, 461381] C737 154) [461381, 741, 21925] C737
61) [881, 1370, 465701] C737 156) [465701, 685, 881] C737
62) [1153, 594, 83597] C737 136) [83597, 297, 1153] C737
63) [1193, 374, 15881] C737 ---) [15881, 187, 4772] C2211
64) [1201, 1758, 292241] C737 149) [292241, 879, 120100] C737
65) [1609, 683, 26116] C737 108) [6529, 1366, 362025] C737
66) [1613, 925, 145757] C737 144) [145757, 1850, 272597] C737
67) [1709, 1706, 556709] C737 158) [556709, 853, 42725] C737
68) [1973, 830, 45953] C737 135) [45953, 415, 31568] C737
69) [2137, 1810, 742093] C737 ---) [6133, 905, 19233] C2211
70) [2221, 1902, 16001] C737 ---) [16001, 951, 222100] C3685
71) [2437, 3598, 2885473] C737 111) [7993, 1799, 87732] C737
72) [2441, 1375, 203536] C737 117) [12721, 2750, 1076481] C737
73) [2689, 1178, 78021] C737 112) [8669, 589, 67225] C737
74) [2729, 4351, 3798800] C737 113) [9497, 3511, 2794496] C737
75) [2729, 1391, 182848] C737 ---) [2857, 2782, 1203489] C2211
76) [2753, 2914, 1847549] C737 125) [15269, 1457, 68825] C737
77) [2753, 3299, 2637572] C737 ---) [13457, 5927, 704768] C9581
78) [2969, 6655, 10804304] C737 119) [13781, 3521, 1855625] C737
79) [3037, 1661, 51201] C737 102) [5689, 3322, 2554117] C737
80) [3037, 706, 15277] C737 ---) [15277, 353, 27333] C5159
81) [3049, 1871, 782928] C737 100) [5437, 3742, 368929] C737
82) [3329, 2410, 373429] C737 110) [7621, 1205, 269649] C737
83) [3361, 486, 5273] C737 ---) [5273, 243, 13444] C5159
84) [3433, 555, 76148] C737 134) [19037, 1110, 3433] C737
85) [3449, 1107, 57172] C737 121) [14293, 2214, 996761] C737
86) [3517, 9045, 17983193] C737 131) [18713, 4967, 2757328] C737
87) [3533, 3597, 3212521] C737 133) [19009, 7194, 88325] C737
88) [3709, 6569, 10787013] C737 122) [14797, 5513, 5641389] C737
89) [3821, 5305, 5995489] C737 109) [7129, 2859, 1528400] C737
90) [4049, 5994, 414325] C737 126) [16573, 2997, 2141921] C737
91) [4049, 5554, 6918125] C737 115) [11069, 2777, 198401] C737
92) [4157, 1381, 18481] C737 130) [18481, 2762, 1833237] C737
93) [4177, 3951, 743744] C737 ---) [11621, 6153, 7021537] C5159
94) [4261, 5441, 3437325] C737 ---) [15277, 7613, 13843989] C5159
95) [4289, 1003, 70292] C737 128) [17573, 2006, 724841] C737
96) [4793, 503, 33296] C737 ---) [2081, 1006, 119825] C3685
97) [4801, 4226, 1219293] C737 123) [15053, 2113, 811369] C737
98) [4957, 2321, 1286037] C737 ---) [15877, 4642, 242893] C9581
99) [4993, 3447, 2969204] C737 124) [15149, 6894, 4993] C737
100) [5437, 3742, 368929] C737 81) [3049, 1871, 782928] C737
101) [5581, 630, 9929] C737 114) [9929, 315, 22324] C737
102) [5689, 3322, 2554117] C737 79) [3037, 1661, 51201] C737
103) [5701, 9769, 2295733] C737 132) [18973, 6709, 1647589] C737
104) [5857, 1731, 220496] C737 118) [13781, 3462, 2114377] C737
105) [5861, 10582, 893417] C737 129) [18233, 5291, 6775316] C737
106) [5869, 8621, 1148013] C737 120) [14173, 4961, 4278501] C737
107) [5981, 8429, 10643125] C737 127) [17029, 9021, 18092525] C737
108) [6529, 1366, 362025] C737 65) [1609, 683, 26116] C737
109) [7129, 2859, 1528400] C737 89) [3821, 5305, 5995489] C737
110) [7621, 1205, 269649] C737 82) [3329, 2410, 373429] C737
111) [7993, 1799, 87732] C737 71) [2437, 3598, 2885473] C737
112) [8669, 589, 67225] C737 73) [2689, 1178, 78021] C737
113) [9497, 3511, 2794496] C737 74) [2729, 4351, 3798800] C737
114) [9929, 315, 22324] C737 101) [5581, 630, 9929] C737
115) [11069, 2777, 198401] C737 91) [4049, 5554, 6918125] C737
116) [12589, 1081, 137925] C737 ---) [613, 2162, 616861] C67
117) [12721, 2750, 1076481] C737 72) [2441, 1375, 203536] C737
118) [13781, 3462, 2114377] C737 104) [5857, 1731, 220496] C737
119) [13781, 3521, 1855625] C737 78) [2969, 6655, 10804304] C737
120) [14173, 4961, 4278501] C737 106) [5869, 8621, 1148013] C737
121) [14293, 2214, 996761] C737 85) [3449, 1107, 57172] C737
122) [14797, 5513, 5641389] C737 88) [3709, 6569, 10787013] C737
123) [15053, 2113, 811369] C737 97) [4801, 4226, 1219293] C737
124) [15149, 6894, 4993] C737 99) [4993, 3447, 2969204] C737
125) [15269, 1457, 68825] C737 76) [2753, 2914, 1847549] C737
126) [16573, 2997, 2141921] C737 90) [4049, 5994, 414325] C737
127) [17029, 9021, 18092525] C737 107) [5981, 8429, 10643125] C737
128) [17573, 2006, 724841] C737 95) [4289, 1003, 70292] C737
129) [18233, 5291, 6775316] C737 105) [5861, 10582, 893417] C737
130) [18481, 2762, 1833237] C737 92) [4157, 1381, 18481] C737
131) [18713, 4967, 2757328] C737 86) [3517, 9045, 17983193] C737
132) [18973, 6709, 1647589] C737 103) [5701, 9769, 2295733] C737
133) [19009, 7194, 88325] C737 87) [3533, 3597, 3212521] C737
134) [19037, 1110, 3433] C737 84) [3433, 555, 76148] C737
135) [45953, 415, 31568] C737 68) [1973, 830, 45953] C737
136) [83597, 297, 1153] C737 62) [1153, 594, 83597] C737
137) [90749, 305, 569] C737 56) [569, 610, 90749] C737
138) [91097, 379, 13136] C737 59) [821, 758, 91097] C737
139) [94961, 479, 33620] C737 ---) [5, 617, 94961] C67
140) [104513, 351, 4672] C737 34) [73, 702, 104513] C737
141) [109313, 639, 74752] C737 31) [73, 1278, 109313] C737
142) [110753, 399, 12112] C737 58) [757, 798, 110753] C737
143) [111773, 337, 449] C737 53) [449, 674, 111773] C737
144) [145757, 1850, 272597] C737 66) [1613, 925, 145757] C737
145) [148781, 441, 11425] C737 54) [457, 882, 148781] C737
146) [178813, 1706, 12357] C737 ---) [1373, 853, 178813] C2211
147) [187469, 513, 18925] C737 57) [757, 1026, 187469] C737
148) [196817, 1979, 536272] C737 48) [277, 3958, 1771353] C737
149) [292241, 879, 120100] C737 64) [1201, 1758, 292241] C737
150) [321721, 643, 22932] C737 ---) [13, 1286, 321721] C67
151) [335417, 2903, 10496] C737 29) [41, 2491, 1341668] C737
152) [361793, 2495, 1465808] C737 50) [317, 4990, 361793] C737
153) [439577, 1915, 806912] C737 46) [197, 3830, 439577] C737
154) [461381, 741, 21925] C737 60) [877, 1482, 461381] C737
155) [461801, 683, 1172] C737 49) [293, 1366, 461801] C737
156) [465701, 685, 881] C737 61) [881, 1370, 465701] C737
157) [539309, 849, 45373] C737 44) [157, 1698, 539309] C737
158) [556709, 853, 42725] C737 67) [1709, 1706, 556709] C737
159) [735113, 859, 692] C737 45) [173, 1718, 735113] C737
160) [871681, 2819, 25408] C737 51) [397, 5638, 7845129] C737
161) [1059713, 1055, 13328] C737 23) [17, 2110, 1059713] C737
162) [1076381, 1041, 1825] C737 35) [73, 2082, 1076381] C737
163) [1076657, 1063, 13328] C737 21) [17, 2126, 1076657] C737
164) [1101509, 1053, 1825] C737 33) [73, 2106, 1101509] C737
165) [1351169, 1791, 464128] C737 25) [37, 3582, 1351169] C737
166) [1458461, 1281, 45625] C737 32) [73, 2562, 1458461] C737
167) [1509457, 1879, 505296] C737 24) [29, 3758, 1509457] C737
168) [1667321, 1739, 339200] C737 30) [53, 3478, 1667321] C737
169) [1883017, 4151, 70912] C737 47) [277, 8302, 16947153] C737
170) [2326921, 3011, 1684800] C737 20) [13, 5041, 2326921] C737
171) [2952881, 2183, 453152] C737 12) [8, 4366, 2952881] C737
172) [4327201, 2287, 225792] C737 13) [8, 4574, 4327201] C737
173) [4374641, 2279, 204800] C737 17) [8, 4558, 4374641] C737
174) [5224937, 2643, 440128] C737 18) [13, 5286, 5224937] C737
175) [5345017, 3019, 942336] C737 52) [409, 6038, 5345017] C737
176) [5618497, 2527, 191808] C737 26) [37, 5054, 5618497] C737
177) [6475289, 2683, 180800] C737 42) [113, 5366, 6475289] C737
178) [7119449, 2907, 332800] C737 19) [13, 5814, 7119449] C737
179) [11617561, 3419, 18000] C737 11) [5, 6838, 11617561] C737
180) [12672641, 3871, 578000] C737 9) [5, 7742, 12672641] C737
181) [14640377, 4171, 689216] C737 37) [89, 8342, 14640377] C737
182) [17286889, 4403, 524880] C737 5) [5, 8806, 17286889] C737
183) [18346673, 4295, 25088] C737 15) [8, 8590, 18346673] C737
184) [18953689, 4763, 933120] C737 3) [5, 9526, 18953689] C737
185) [21333881, 4619, 320] C737 1) [5, 9238, 21333881] C737
186) [23285569, 5087, 648000] C737 8) [5, 10174, 23285569] C737
187) [27906553, 5291, 22032] C737 22) [17, 10582, 27906553] C737
188) [31997569, 5663, 18000] C737 6) [5, 11326, 31997569] C737
189) [34234841, 6011, 474320] C737 2) [5, 12022, 34234841] C737