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 ■