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 5 non-normal (D4) quartic CM field invariants: 215 fields

K Quartic invariants Cl(OK) Igusa invariants Kr Reflex invariants Cl(OKr) Igusa invariants
1) [5, 94, 1889] C5 167) [1889, 47, 80] C5
2) [5, 73, 1301] C5 158) [1301, 61, 605] C5
3) [5, 161, 6029] C5 211) [6029, 97, 845] C5
4) [5, 69, 1129] C5 ---) [1129, 43, 180] C45
5) [5, 122, 3701] C5 195) [3701, 61, 5] C5
6) [5, 169, 6229] C5 212) [6229, 93, 605] C5
7) [5, 154, 5749] C5 209) [5749, 77, 45] C5
8) [5, 113, 2741] C5 183) [2741, 61, 245] C5
9) [5, 97, 2141] C5 172) [2141, 89, 1445] C5
10) [5, 109, 2609] C5 181) [2609, 103, 2000] C5
11) [5, 149, 5189] C5 204) [5189, 133, 3125] C5
12) [5, 146, 4349] C5 202) [4349, 73, 245] C5
13) [5, 114, 2749] C5 184) [2749, 57, 125] C5
14) [5, 129, 3709] C5 196) [3709, 73, 405] C5
15) [5, 169, 7109] C5 214) [7109, 133, 2645] C5
16) [5, 149, 4889] C5 ---) [4889, 83, 500] C5 x C5
17) [5, 146, 5309] C5 206) [5309, 73, 5] C5
18) [5, 194, 7789] C5 215) [7789, 97, 405] C5
19) [5, 77, 1381] C5 160) [1381, 69, 845] C5
20) [5, 81, 1609] C5 163) [1609, 67, 720] C5
21) [5, 109, 2909] C5 187) [2909, 73, 605] C5
22) [5, 97, 2341] C5 175) [2341, 69, 605] C5
23) [5, 114, 3229] C5 ---) [3229, 57, 5] C15
24) [5, 94, 2129] C5 170) [2129, 47, 20] C5
25) [5, 53, 601] C5 139) [601, 51, 500] C5
26) [5, 53, 641] C5 140) [641, 31, 80] C5
27) [5, 121, 3109] C5 189) [3109, 117, 2645] C5
28) [5, 157, 5501] C5 207) [5501, 89, 605] C5
29) [5, 62, 881] C5 147) [881, 31, 20] C5
30) [8, 182, 4409] C5 ---) [4409, 91, 968] C45
31) [8, 98, 1753] C5 166) [1753, 49, 162] C5
32) [8, 82, 1289] C5 157) [1289, 41, 98] C5
33) [8, 30, 193] C5 117) [193, 15, 8] C5
34) [8, 162, 3673] C5 193) [3673, 81, 722] C5
35) [8, 146, 3529] C5 191) [3529, 73, 450] C5
36) [8, 58, 449] C5 134) [449, 29, 98] C5
37) [8, 166, 6857] C5 213) [6857, 83, 8] C5
38) [8, 130, 4217] C5 201) [4217, 65, 2] C5
39) [8, 114, 2281] C5 174) [2281, 57, 242] C5
40) [8, 118, 1913] C5 168) [1913, 59, 392] C5
41) [8, 134, 2441] C5 178) [2441, 67, 512] C5
42) [8, 42, 241] C5 123) [241, 21, 50] C5
43) [8, 134, 4457] C5 203) [4457, 67, 8] C5
44) [8, 130, 3833] C5 198) [3833, 65, 98] C5
45) [8, 82, 1609] C5 164) [1609, 41, 18] C5
46) [8, 166, 5737] C5 208) [5737, 83, 288] C5
47) [8, 102, 2089] C5 ---) [2089, 51, 128] C15
48) [13, 69, 797] C5 144) [797, 85, 13] C5
49) [13, 81, 701] C5 143) [701, 57, 637] C5
50) [13, 89, 1249] C5 156) [1249, 107, 52] C5
51) [13, 122, 3253] C5 ---) [3253, 61, 117] C5 x C5
52) [13, 110, 1153] C5 154) [1153, 55, 468] C5
53) [13, 194, 5197] C5 205) [5197, 97, 1053] C5
54) [13, 81, 1637] C5 165) [1637, 145, 1573] C5
55) [13, 185, 3613] C5 192) [3613, 197, 1573] C5
56) [13, 69, 1109] C5 153) [1109, 137, 2197] C5
57) [13, 149, 3181] C5 ---) [3181, 173, 325] C5 x C5
58) [13, 57, 653] C5 141) [653, 77, 13] C5
59) [13, 134, 2617] C5 182) [2617, 67, 468] C5
60) [17, 223, 11204] C5 186) [2801, 127, 3332] C5
61) [17, 166, 5801] C5 210) [5801, 83, 272] C5
62) [17, 182, 3929] C5 199) [3929, 91, 1088] C5
63) [17, 126, 3697] C5 194) [3697, 63, 68] C5
64) [17, 110, 2753] C5 185) [2753, 55, 68] C5
65) [17, 230, 3433] C5 190) [3433, 115, 2448] C5
66) [17, 142, 2593] C5 180) [2593, 71, 612] C5
67) [17, 58, 229] C5 ---) [229, 29, 153] C15
68) [17, 79, 1556] C5 129) [389, 61, 833] C5
69) [17, 118, 2393] C5 177) [2393, 59, 272] C5
70) [17, 247, 15044] C5 197) [3761, 223, 11492] C5
71) [29, 161, 1949] C5 169) [1949, 221, 29] C5
72) [29, 25, 149] C5 114) [149, 50, 29] C5
73) [29, 105, 661] C5 142) [661, 129, 29] C5
74) [29, 37, 277] C5 124) [277, 74, 261] C5
75) [29, 77, 257] C5 ---) [257, 83, 116] C15
76) [37, 138, 1061] C5 151) [1061, 69, 925] C5
77) [37, 42, 293] C5 125) [293, 21, 37] C5
78) [37, 54, 137] C5 113) [137, 27, 148] C5
79) [37, 122, 2389] C5 176) [2389, 61, 333] C5
80) [37, 98, 1069] C5 152) [1069, 49, 333] C5
81) [41, 214, 953] C5 150) [953, 107, 2624] C5
82) [41, 94, 1553] C5 162) [1553, 47, 164] C5
83) [41, 167, 5732] C5 161) [1433, 191, 164] C5
84) [41, 87, 1636] C5 132) [409, 127, 1476] C5
85) [41, 50, 461] C5 136) [461, 25, 41] C5
86) [41, 286, 4049] C5 200) [4049, 143, 4100] C5
87) [41, 150, 3001] C5 188) [3001, 75, 656] C5
88) [53, 62, 113] C5 112) [113, 31, 212] C5
89) [53, 29, 197] C5 119) [197, 58, 53] C5
90) [53, 21, 97] C5 106) [97, 42, 53] C5
91) [53, 42, 229] C5 ---) [229, 21, 53] C15
92) [53, 41, 89] C5 101) [89, 59, 848] C5
93) [61, 42, 197] C5 120) [197, 21, 61] C5
94) [61, 178, 7677] C5 146) [853, 89, 61] C5
95) [61, 221, 1093] C5 ---) [1093, 217, 4941] C5 x C5
96) [73, 195, 9488] C5 138) [593, 155, 4672] C5
97) [73, 159, 3236] C5 145) [809, 191, 7300] C5
98) [73, 171, 6416] C5 ---) [401, 91, 1168] C5 x C5
99) [73, 422, 2473] C5 179) [2473, 211, 10512] C5
100) [89, 166, 1193] C5 155) [1193, 83, 1424] C5
101) [89, 59, 848] C5 92) [53, 41, 89] C5
102) [89, 110, 1601] C5 ---) [1601, 55, 356] C35
103) [97, 371, 34192] C5 171) [2137, 455, 46948] C5
104) [97, 254, 2161] C5 173) [2161, 127, 3492] C5
105) [97, 158, 4689] C5 137) [521, 79, 388] C5
106) [97, 42, 53] C5 90) [53, 21, 97] C5
107) [101, 146, 4925] C5 118) [197, 73, 101] C5
108) [109, 229, 12429] C5 159) [1381, 365, 5341] C5
109) [109, 118, 1737] C5 116) [193, 59, 436] C5
110) [113, 63, 964] C5 121) [241, 126, 113] C5
111) [113, 283, 15248] C5 149) [953, 275, 7232] C5
112) [113, 31, 212] C5 88) [53, 62, 113] C5
113) [137, 27, 148] C5 78) [37, 54, 137] C5
114) [149, 50, 29] C5 72) [29, 25, 149] C5
115) [181, 125, 241] C5 122) [241, 235, 6516] C5
116) [193, 59, 436] C5 109) [109, 118, 1737] C5
117) [193, 15, 8] C5 33) [8, 30, 193] C5
118) [197, 73, 101] C5 107) [101, 146, 4925] C5
119) [197, 58, 53] C5 89) [53, 29, 197] C5
120) [197, 21, 61] C5 93) [61, 42, 197] C5
121) [241, 126, 113] C5 110) [113, 63, 964] C5
122) [241, 235, 6516] C5 115) [181, 125, 241] C5
123) [241, 21, 50] C5 42) [8, 42, 241] C5
124) [277, 74, 261] C5 74) [29, 37, 277] C5
125) [293, 21, 37] C5 77) [37, 42, 293] C5
126) [313, 515, 59968] C5 148) [937, 395, 20032] C5
127) [313, 227, 6544] C5 131) [409, 359, 31300] C5
128) [337, 287, 1636] C5 130) [409, 343, 12132] C5
129) [389, 61, 833] C5 68) [17, 79, 1556] C5
130) [409, 343, 12132] C5 128) [337, 287, 1636] C5
131) [409, 359, 31300] C5 127) [313, 227, 6544] C5
132) [409, 127, 1476] C5 84) [41, 87, 1636] C5
133) [433, 295, 16452] C5 135) [457, 343, 15588] C5
134) [449, 29, 98] C5 36) [8, 58, 449] C5
135) [457, 343, 15588] C5 133) [433, 295, 16452] C5
136) [461, 25, 41] C5 85) [41, 50, 461] C5
137) [521, 79, 388] C5 105) [97, 158, 4689] C5
138) [593, 155, 4672] C5 96) [73, 195, 9488] C5
139) [601, 51, 500] C5 25) [5, 53, 601] C5
140) [641, 31, 80] C5 26) [5, 53, 641] C5
141) [653, 77, 13] C5 58) [13, 57, 653] C5
142) [661, 129, 29] C5 73) [29, 105, 661] C5
143) [701, 57, 637] C5 49) [13, 81, 701] C5
144) [797, 85, 13] C5 48) [13, 69, 797] C5
145) [809, 191, 7300] C5 97) [73, 159, 3236] C5
146) [853, 89, 61] C5 94) [61, 178, 7677] C5
147) [881, 31, 20] C5 29) [5, 62, 881] C5
148) [937, 395, 20032] C5 126) [313, 515, 59968] C5
149) [953, 275, 7232] C5 111) [113, 283, 15248] C5
150) [953, 107, 2624] C5 81) [41, 214, 953] C5
151) [1061, 69, 925] C5 76) [37, 138, 1061] C5
152) [1069, 49, 333] C5 80) [37, 98, 1069] C5
153) [1109, 137, 2197] C5 56) [13, 69, 1109] C5
154) [1153, 55, 468] C5 52) [13, 110, 1153] C5
155) [1193, 83, 1424] C5 100) [89, 166, 1193] C5
156) [1249, 107, 52] C5 50) [13, 89, 1249] C5
157) [1289, 41, 98] C5 32) [8, 82, 1289] C5
158) [1301, 61, 605] C5 2) [5, 73, 1301] C5
159) [1381, 365, 5341] C5 108) [109, 229, 12429] C5
160) [1381, 69, 845] C5 19) [5, 77, 1381] C5
161) [1433, 191, 164] C5 83) [41, 167, 5732] C5
162) [1553, 47, 164] C5 82) [41, 94, 1553] C5
163) [1609, 67, 720] C5 20) [5, 81, 1609] C5
164) [1609, 41, 18] C5 45) [8, 82, 1609] C5
165) [1637, 145, 1573] C5 54) [13, 81, 1637] C5
166) [1753, 49, 162] C5 31) [8, 98, 1753] C5
167) [1889, 47, 80] C5 1) [5, 94, 1889] C5
168) [1913, 59, 392] C5 40) [8, 118, 1913] C5
169) [1949, 221, 29] C5 71) [29, 161, 1949] C5
170) [2129, 47, 20] C5 24) [5, 94, 2129] C5
171) [2137, 455, 46948] C5 103) [97, 371, 34192] C5
172) [2141, 89, 1445] C5 9) [5, 97, 2141] C5
173) [2161, 127, 3492] C5 104) [97, 254, 2161] C5
174) [2281, 57, 242] C5 39) [8, 114, 2281] C5
175) [2341, 69, 605] C5 22) [5, 97, 2341] C5
176) [2389, 61, 333] C5 79) [37, 122, 2389] C5
177) [2393, 59, 272] C5 69) [17, 118, 2393] C5
178) [2441, 67, 512] C5 41) [8, 134, 2441] C5
179) [2473, 211, 10512] C5 99) [73, 422, 2473] C5
180) [2593, 71, 612] C5 66) [17, 142, 2593] C5
181) [2609, 103, 2000] C5 10) [5, 109, 2609] C5
182) [2617, 67, 468] C5 59) [13, 134, 2617] C5
183) [2741, 61, 245] C5 8) [5, 113, 2741] C5
184) [2749, 57, 125] C5 13) [5, 114, 2749] C5
185) [2753, 55, 68] C5 64) [17, 110, 2753] C5
186) [2801, 127, 3332] C5 60) [17, 223, 11204] C5
187) [2909, 73, 605] C5 21) [5, 109, 2909] C5
188) [3001, 75, 656] C5 87) [41, 150, 3001] C5
189) [3109, 117, 2645] C5 27) [5, 121, 3109] C5
190) [3433, 115, 2448] C5 65) [17, 230, 3433] C5
191) [3529, 73, 450] C5 35) [8, 146, 3529] C5
192) [3613, 197, 1573] C5 55) [13, 185, 3613] C5
193) [3673, 81, 722] C5 34) [8, 162, 3673] C5
194) [3697, 63, 68] C5 63) [17, 126, 3697] C5
195) [3701, 61, 5] C5 5) [5, 122, 3701] C5
196) [3709, 73, 405] C5 14) [5, 129, 3709] C5
197) [3761, 223, 11492] C5 70) [17, 247, 15044] C5
198) [3833, 65, 98] C5 44) [8, 130, 3833] C5
199) [3929, 91, 1088] C5 62) [17, 182, 3929] C5
200) [4049, 143, 4100] C5 86) [41, 286, 4049] C5
201) [4217, 65, 2] C5 38) [8, 130, 4217] C5
202) [4349, 73, 245] C5 12) [5, 146, 4349] C5
203) [4457, 67, 8] C5 43) [8, 134, 4457] C5
204) [5189, 133, 3125] C5 11) [5, 149, 5189] C5
205) [5197, 97, 1053] C5 53) [13, 194, 5197] C5
206) [5309, 73, 5] C5 17) [5, 146, 5309] C5
207) [5501, 89, 605] C5 28) [5, 157, 5501] C5
208) [5737, 83, 288] C5 46) [8, 166, 5737] C5
209) [5749, 77, 45] C5 7) [5, 154, 5749] C5
210) [5801, 83, 272] C5 61) [17, 166, 5801] C5
211) [6029, 97, 845] C5 3) [5, 161, 6029] C5
212) [6229, 93, 605] C5 6) [5, 169, 6229] C5
213) [6857, 83, 8] C5 37) [8, 166, 6857] C5
214) [7109, 133, 2645] C5 15) [5, 169, 7109] C5
215) [7789, 97, 405] C5 18) [5, 194, 7789] C5