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 2 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, 29, 209] C2 162) [209, 23, 80] C2
2) [5, 61, 869] C2 201) [869, 37, 125] C2
3) [5, 69, 1189] C2 ---) [1189, 53, 405] C2 x C2
4) [5, 9, 19] C2 128) [76, 18, 5] C2
5) [5, 25, 145] C2 ---) [145, 15, 20] C8
6) [5, 45, 445] C2 ---) [445, 25, 45] C8
7) [5, 66, 909] C2 140) [101, 33, 45] C2
8) [5, 16, 59] C2 167) [236, 32, 20] C2
9) [5, 14, 44] C2 112) [44, 8, 5] C2
10) [5, 49, 589] C2 196) [589, 33, 125] C2
11) [5, 37, 341] C2 180) [341, 29, 125] C2
12) [5, 11, 29] C2 89) [29, 7, 5] C2
13) [5, 33, 261] C2 90) [29, 21, 45] C2
14) [5, 74, 1349] C2 205) [1349, 37, 5] C2
15) [5, 7, 11] C2 113) [44, 14, 5] C2
16) [8, 38, 329] C2 176) [329, 19, 8] C2
17) [8, 50, 553] C2 195) [553, 25, 18] C2
18) [8, 10, 23] C2 135) [92, 10, 2] C2
19) [8, 6, 7] C2 79) [28, 6, 2] C2
20) [8, 8, 14] C2 116) [56, 8, 2] C2
21) [8, 14, 41] C2 109) [41, 7, 2] C2
22) [8, 70, 713] C2 199) [713, 35, 128] C2
23) [8, 54, 697] C2 ---) [697, 27, 8] C2 x C6
24) [8, 34, 217] C2 165) [217, 17, 18] C2
25) [8, 86, 1337] C2 204) [1337, 43, 128] C2
26) [8, 66, 1017] C2 143) [113, 33, 18] C2
27) [8, 50, 425] C2 54) [17, 25, 50] C2
28) [8, 26, 137] C2 148) [137, 13, 8] C2
29) [12, 30, 177] C2 155) [177, 15, 12] C2
30) [12, 10, 13] C2 47) [13, 5, 3] C2
31) [12, 98, 673] C2 198) [673, 49, 432] C2
32) [12, 26, 61] C2 124) [61, 13, 27] C2
33) [12, 14, 22] C2 132) [88, 10, 3] C2
34) [12, 62, 913] C2 202) [913, 31, 12] C2
35) [12, 14, 37] C2 103) [37, 7, 3] C2
36) [12, 8, 13] C2 49) [13, 10, 12] C2
37) [12, 26, 157] C2 152) [157, 13, 3] C2
38) [12, 66, 321] C2 ---) [321, 33, 192] C6
39) [12, 6, 6] C2 75) [24, 6, 3] C2
40) [12, 18, 33] C2 98) [33, 9, 12] C2
41) [12, 42, 393] C2 183) [393, 21, 12] C2
42) [12, 74, 937] C2 203) [937, 37, 108] C2
43) [12, 54, 537] C2 193) [537, 27, 48] C2
44) [12, 34, 97] C2 138) [97, 17, 48] C2
45) [12, 50, 433] C2 189) [433, 25, 48] C2
46) [13, 74, 901] C2 ---) [901, 37, 117] C8
47) [13, 5, 3] C2 30) [12, 10, 13] C2
48) [13, 17, 43] C2 153) [172, 34, 117] C2
49) [13, 10, 12] C2 36) [12, 8, 13] C2
50) [13, 61, 381] C2 181) [381, 41, 325] C2
51) [13, 49, 597] C2 197) [597, 89, 637] C2
52) [13, 34, 237] C2 168) [237, 17, 13] C2
53) [13, 17, 69] C2 125) [69, 33, 117] C2
54) [17, 25, 50] C2 27) [8, 50, 425] C2
55) [17, 31, 236] C2 166) [236, 62, 17] C2
56) [17, 62, 689] C2 ---) [689, 31, 68] C8
57) [17, 37, 134] C2 192) [536, 74, 833] C2
58) [17, 17, 34] C2 ---) [136, 34, 153] C4
59) [17, 20, 83] C2 178) [332, 40, 68] C2
60) [17, 28, 43] C2 154) [172, 56, 612] C2
61) [17, 13, 38] C2 151) [152, 26, 17] C2
62) [21, 65, 421] C2 187) [421, 85, 1701] C2
63) [21, 53, 445] C2 ---) [445, 106, 1029] C8
64) [21, 37, 85] C2 ---) [85, 29, 189] C4
65) [21, 29, 205] C2 ---) [205, 58, 21] C4
66) [21, 50, 541] C2 194) [541, 25, 21] C2
67) [21, 53, 277] C2 173) [277, 57, 189] C2
68) [21, 26, 85] C2 ---) [85, 13, 21] C4
69) [21, 13, 37] C2 101) [37, 26, 21] C2
70) [24, 92, 2020] C2 ---) [505, 46, 24] C8
71) [24, 26, 145] C2 ---) [145, 13, 6] C8
72) [24, 38, 265] C2 ---) [265, 19, 24] C4
73) [24, 8, 10] C2 ---) [40, 16, 24] C4
74) [24, 74, 769] C2 200) [769, 37, 150] C2
75) [24, 6, 3] C2 39) [12, 6, 6] C2
76) [24, 20, 76] C2 129) [76, 10, 6] C2
77) [24, 68, 772] C2 159) [193, 34, 96] C2
78) [24, 86, 313] C2 175) [313, 43, 384] C2
79) [28, 6, 2] C2 19) [8, 6, 7] C2
80) [28, 34, 177] C2 157) [177, 17, 28] C2
81) [28, 128, 1828] C2 190) [457, 64, 567] C2
82) [28, 46, 417] C2 186) [417, 23, 28] C2
83) [28, 32, 228] C2 120) [57, 16, 7] C2
84) [28, 58, 393] C2 182) [393, 29, 112] C2
85) [28, 64, 996] C2 171) [249, 32, 7] C2
86) [28, 30, 113] C2 144) [113, 15, 28] C2
87) [28, 80, 1348] C2 179) [337, 40, 63] C2
88) [29, 17, 65] C2 ---) [65, 34, 29] C2 x C2
89) [29, 7, 5] C2 12) [5, 11, 29] C2
90) [29, 21, 45] C2 13) [5, 33, 261] C2
91) [33, 35, 232] C2 ---) [232, 70, 297] C4
92) [33, 50, 328] C2 ---) [328, 100, 1188] C8
93) [33, 23, 124] C2 146) [124, 46, 33] C2
94) [33, 62, 433] C2 188) [433, 31, 132] C2
95) [33, 26, 37] C2 100) [37, 13, 33] C2
96) [33, 41, 412] C2 185) [412, 82, 33] C2
97) [33, 71, 1252] C2 174) [313, 87, 1188] C2
98) [33, 9, 12] C2 40) [12, 18, 33] C2
99) [33, 20, 67] C2 172) [268, 40, 132] C2
100) [37, 13, 33] C2 95) [33, 26, 37] C2
101) [37, 26, 21] C2 69) [21, 13, 37] C2
102) [37, 34, 141] C2 150) [141, 17, 37] C2
103) [37, 7, 3] C2 35) [12, 14, 37] C2
104) [37, 73, 213] C2 163) [213, 57, 333] C2
105) [37, 53, 693] C2 131) [77, 29, 37] C2
106) [41, 35, 296] C2 ---) [296, 70, 41] C2 x C2
107) [41, 16, 23] C2 136) [92, 32, 164] C2
108) [41, 9, 10] C2 ---) [40, 18, 41] C2 x C2
109) [41, 7, 2] C2 21) [8, 14, 41] C2
110) [41, 62, 305] C2 ---) [305, 31, 164] C4
111) [41, 39, 124] C2 145) [124, 78, 1025] C2
112) [44, 8, 5] C2 9) [5, 14, 44] C2
113) [44, 14, 5] C2 15) [5, 7, 11] C2
114) [44, 104, 1604] C2 ---) [401, 52, 275] C10
115) [53, 34, 77] C2 130) [77, 17, 53] C2
116) [56, 8, 2] C2 20) [8, 8, 14] C2
117) [56, 44, 260] C2 ---) [65, 22, 56] C4
118) [56, 26, 113] C2 142) [113, 13, 14] C2
119) [57, 17, 58] C2 ---) [232, 34, 57] C4
120) [57, 16, 7] C2 83) [28, 32, 228] C2
121) [57, 167, 1828] C2 191) [457, 111, 2052] C2
122) [61, 98, 205] C2 ---) [205, 49, 549] C4
123) [61, 25, 141] C2 149) [141, 50, 61] C2
124) [61, 13, 27] C2 32) [12, 26, 61] C2
125) [69, 33, 117] C2 53) [13, 17, 69] C2
126) [69, 77, 85] C2 ---) [85, 49, 69] C4
127) [73, 29, 46] C2 158) [184, 58, 657] C2
128) [76, 18, 5] C2 4) [5, 9, 19] C2
129) [76, 10, 6] C2 76) [24, 20, 76] C2
130) [77, 17, 53] C2 115) [53, 34, 77] C2
131) [77, 29, 37] C2 105) [37, 53, 693] C2
132) [88, 10, 3] C2 33) [12, 14, 22] C2
133) [88, 70, 873] C2 139) [97, 35, 88] C2
134) [89, 27, 160] C2 ---) [40, 54, 89] C2 x C2
135) [92, 10, 2] C2 18) [8, 10, 23] C2
136) [92, 32, 164] C2 107) [41, 16, 23] C2
137) [93, 69, 981] C2 141) [109, 97, 2325] C2
138) [97, 17, 48] C2 44) [12, 34, 97] C2
139) [97, 35, 88] C2 133) [88, 70, 873] C2
140) [101, 33, 45] C2 7) [5, 66, 909] C2
141) [109, 97, 2325] C2 137) [93, 69, 981] C2
142) [113, 13, 14] C2 118) [56, 26, 113] C2
143) [113, 33, 18] C2 26) [8, 66, 1017] C2
144) [113, 15, 28] C2 86) [28, 30, 113] C2
145) [124, 78, 1025] C2 111) [41, 39, 124] C2
146) [124, 46, 33] C2 93) [33, 23, 124] C2
147) [129, 26, 40] C2 ---) [40, 52, 516] C4
148) [137, 13, 8] C2 28) [8, 26, 137] C2
149) [141, 50, 61] C2 123) [61, 25, 141] C2
150) [141, 17, 37] C2 102) [37, 34, 141] C2
151) [152, 26, 17] C2 61) [17, 13, 38] C2
152) [157, 13, 3] C2 37) [12, 26, 157] C2
153) [172, 34, 117] C2 48) [13, 17, 43] C2
154) [172, 56, 612] C2 60) [17, 28, 43] C2
155) [177, 15, 12] C2 29) [12, 30, 177] C2
156) [177, 110, 193] C2 160) [193, 55, 708] C2
157) [177, 17, 28] C2 80) [28, 34, 177] C2
158) [184, 58, 657] C2 127) [73, 29, 46] C2
159) [193, 34, 96] C2 77) [24, 68, 772] C2
160) [193, 55, 708] C2 156) [177, 110, 193] C2
161) [193, 142, 1953] C2 164) [217, 71, 772] C2
162) [209, 23, 80] C2 1) [5, 29, 209] C2
163) [213, 57, 333] C2 104) [37, 73, 213] C2
164) [217, 71, 772] C2 161) [193, 142, 1953] C2
165) [217, 17, 18] C2 24) [8, 34, 217] C2
166) [236, 62, 17] C2 55) [17, 31, 236] C2
167) [236, 32, 20] C2 8) [5, 16, 59] C2
168) [237, 17, 13] C2 52) [13, 34, 237] C2
169) [241, 107, 2320] C2 ---) [145, 191, 964] C8
170) [249, 17, 10] C2 ---) [40, 34, 249] C4
171) [249, 32, 7] C2 85) [28, 64, 996] C2
172) [268, 40, 132] C2 99) [33, 20, 67] C2
173) [277, 57, 189] C2 67) [21, 53, 277] C2
174) [313, 87, 1188] C2 97) [33, 71, 1252] C2
175) [313, 43, 384] C2 78) [24, 86, 313] C2
176) [329, 19, 8] C2 16) [8, 38, 329] C2
177) [329, 67, 1040] C2 ---) [65, 134, 329] C4
178) [332, 40, 68] C2 59) [17, 20, 83] C2
179) [337, 40, 63] C2 87) [28, 80, 1348] C2
180) [341, 29, 125] C2 11) [5, 37, 341] C2
181) [381, 41, 325] C2 50) [13, 61, 381] C2
182) [393, 29, 112] C2 84) [28, 58, 393] C2
183) [393, 21, 12] C2 41) [12, 42, 393] C2
184) [409, 43, 360] C2 ---) [40, 86, 409] C2 x C2
185) [412, 82, 33] C2 96) [33, 41, 412] C2
186) [417, 23, 28] C2 82) [28, 46, 417] C2
187) [421, 85, 1701] C2 62) [21, 65, 421] C2
188) [433, 31, 132] C2 94) [33, 62, 433] C2
189) [433, 25, 48] C2 45) [12, 50, 433] C2
190) [457, 64, 567] C2 81) [28, 128, 1828] C2
191) [457, 111, 2052] C2 121) [57, 167, 1828] C2
192) [536, 74, 833] C2 57) [17, 37, 134] C2
193) [537, 27, 48] C2 43) [12, 54, 537] C2
194) [541, 25, 21] C2 66) [21, 50, 541] C2
195) [553, 25, 18] C2 17) [8, 50, 553] C2
196) [589, 33, 125] C2 10) [5, 49, 589] C2
197) [597, 89, 637] C2 51) [13, 49, 597] C2
198) [673, 49, 432] C2 31) [12, 98, 673] C2
199) [713, 35, 128] C2 22) [8, 70, 713] C2
200) [769, 37, 150] C2 74) [24, 74, 769] C2
201) [869, 37, 125] C2 2) [5, 61, 869] C2
202) [913, 31, 12] C2 34) [12, 62, 913] C2
203) [937, 37, 108] C2 42) [12, 74, 937] C2
204) [1337, 43, 128] C2 25) [8, 86, 1337] C2
205) [1349, 37, 5] C2 14) [5, 74, 1349] C2