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 C671 non-normal (D4) quartic CM field invariants: 208 fields

K Quartic invariants Cl(OK) Igusa invariants Kr Reflex invariants Cl(OKr) Igusa invariants
1) [5, 8038, 15000361] C671 ---) [15000361, 4019, 288000] C2013
2) [5, 9526, 20346889] C671 204) [20346889, 4763, 584820] C671
3) [5, 7046, 11579209] C671 197) [11579209, 3523, 208080] C671
4) [5, 11174, 27686569] C671 207) [27686569, 5587, 882000] C671
5) [5, 5878, 7485721] C671 188) [7485721, 2939, 288000] C671
6) [5, 12086, 33089929] C671 ---) [33089929, 6043, 856980] C2013
7) [5, 11846, 34953929] C671 208) [34953929, 5923, 32000] C671
8) [5, 9566, 21483169] C671 206) [21483169, 4783, 348480] C671
9) [5, 10078, 22913441] C671 ---) [22913441, 5039, 619520] C11 x C671
10) [5, 9214, 19124929] C671 202) [19124929, 4607, 524880] C671
11) [5, 9158, 20966921] C671 205) [20966921, 4579, 80] C671
12) [5, 7337, 11080841] C671 196) [11080841, 3779, 800000] C671
13) [5, 6573, 9689521] C671 192) [9689521, 3751, 1095120] C671
14) [8, 7214, 12383249] C671 198) [12383249, 3607, 156800] C671
15) [8, 5870, 7711057] C671 ---) [7711057, 2935, 225792] C3355
16) [8, 5870, 8581457] C671 ---) [8581457, 2935, 8192] C2013
17) [8, 7198, 12551393] C671 ---) [12551393, 3599, 100352] C3355
18) [8, 4766, 4919777] C671 ---) [4919777, 2383, 189728] C2013
19) [8, 5758, 8220929] C671 191) [8220929, 2879, 16928] C671
20) [8, 5966, 7838321] C671 190) [7838321, 2983, 264992] C671
21) [8, 4622, 4349489] C671 180) [4349489, 2311, 247808] C671
22) [8, 5486, 7482577] C671 187) [7482577, 2743, 10368] C671
23) [8, 4430, 4711537] C671 181) [4711537, 2215, 48672] C671
24) [13, 9518, 19345873] C671 203) [19345873, 4759, 825552] C671
25) [13, 3918, 3816881] C671 179) [3816881, 1959, 5200] C671
26) [13, 5022, 5652833] C671 184) [5652833, 2511, 163072] C671
27) [17, 2542, 1180241] C671 176) [1180241, 1271, 108800] C671
28) [17, 2734, 754577] C671 174) [754577, 1367, 278528] C671
29) [29, 6382, 10175057] C671 194) [10175057, 3191, 1856] C671
30) [41, 3155, 2436836] C671 ---) [609209, 3959, 110864] C31537
31) [41, 8374, 16680793] C671 201) [16680793, 4187, 212544] C671
32) [41, 1894, 880409] C671 175) [880409, 947, 4100] C671
33) [41, 838, 169657] C671 160) [169657, 419, 1476] C671
34) [53, 2150, 1152233] C671 ---) [1152233, 1075, 848] C3355
35) [53, 4089, 415801] C671 169) [415801, 2699, 1717200] C671
36) [53, 5030, 5660393] C671 185) [5660393, 2515, 166208] C671
37) [61, 4622, 5200177] C671 183) [5200177, 2311, 35136] C671
38) [73, 654, 88241] C671 156) [88241, 327, 4672] C671
39) [73, 5286, 6980777] C671 186) [6980777, 2643, 1168] C671
40) [73, 6534, 10598537] C671 195) [10598537, 3267, 18688] C671
41) [89, 1190, 352601] C671 168) [352601, 595, 356] C671
42) [89, 566, 67273] C671 153) [67273, 283, 3204] C671
43) [89, 1618, 645581] C671 172) [645581, 809, 2225] C671
44) [97, 7734, 10086617] C671 193) [10086617, 3867, 1216768] C671
45) [101, 5721, 8161225] C671 167) [326449, 2947, 130896] C671
46) [113, 5542, 6955241] C671 ---) [6955241, 2771, 180800] C2013
47) [113, 6182, 7702889] C671 189) [7702889, 3091, 462848] C671
48) [113, 7174, 12837641] C671 199) [12837641, 3587, 7232] C671
49) [113, 7990, 15497177] C671 200) [15497177, 3995, 115712] C671
50) [113, 1550, 137777] C671 158) [137777, 775, 115712] C671
51) [173, 3502, 574801] C671 171) [574801, 1751, 622800] C671
52) [181, 2089, 1071025] C671 151) [42841, 1939, 72400] C671
53) [193, 1290, 285557] C671 165) [285557, 645, 32617] C671
54) [197, 3982, 736433] C671 173) [736433, 1991, 806912] C671
55) [233, 5158, 5160041] C671 182) [5160041, 2579, 372800] C671
56) [269, 6094, 3706225] C671 ---) [148249, 3047, 1394496] C2013
57) [269, 1414, 482633] C671 ---) [482633, 707, 4304] C3355
58) [269, 7958, 15815225] C671 ---) [632609, 3979, 4304] C6039
59) [373, 3230, 1748833] C671 178) [1748833, 1615, 214848] C671
60) [409, 5334, 4495289] C671 ---) [4495289, 2667, 654400] C3355
61) [409, 2646, 1724153] C671 177) [1724153, 1323, 6544] C671
62) [557, 1402, 221813] C671 164) [221813, 701, 67397] C671
63) [601, 510, 26561] C671 150) [26561, 255, 9616] C671
64) [773, 886, 183881] C671 ---) [183881, 443, 3092] C2013
65) [773, 1966, 174737] C671 162) [174737, 983, 197888] C671
66) [773, 1129, 313829] C671 166) [313829, 2258, 19325] C671
67) [881, 326, 12473] C671 127) [12473, 163, 3524] C671
68) [929, 935, 199744] C671 ---) [3121, 1731, 92900] C3355
69) [941, 1093, 194917] C671 163) [194917, 2186, 414981] C671
70) [1049, 1038, 202225] C671 119) [8089, 519, 16784] C671
71) [1297, 351, 14912] C671 ---) [233, 431, 20752] C61
72) [1297, 1202, 314509] C671 ---) [1861, 601, 11673] C61
73) [1613, 781, 148861] C671 159) [148861, 1562, 14517] C671
74) [2237, 1118, 169313] C671 ---) [169313, 559, 35792] C2013
75) [2269, 5457, 2107457] C671 ---) [17417, 4623, 9076] C2013
76) [2281, 3455, 424404] C671 ---) [11789, 4017, 2192041] C2013
77) [2297, 5615, 1059392] C671 ---) [16553, 5663, 2352128] C2013
78) [2381, 874, 105253] C671 157) [105253, 437, 21429] C671
79) [2393, 3614, 1886881] C671 118) [6529, 1807, 344592] C671
80) [2393, 554, 67157] C671 152) [67157, 277, 2393] C671
81) [2437, 3881, 153297] C671 ---) [17033, 6891, 1647412] C3355
82) [2593, 3659, 1090512] C671 ---) [7573, 3581, 23337] C6039
83) [2789, 1545, 10369] C671 122) [10369, 3090, 2345549] C671
84) [2837, 610, 81677] C671 155) [81677, 305, 2837] C671
85) [3037, 1058, 170509] C671 161) [170509, 529, 27333] C671
86) [3037, 3534, 12401] C671 ---) [12401, 1767, 777472] C2013
87) [3049, 3755, 2243664] C671 140) [15581, 6633, 8564641] C671
88) [3061, 821, 131013] C671 135) [14557, 1642, 149989] C671
89) [3209, 5163, 1657300] C671 143) [16573, 5553, 7704809] C671
90) [3449, 3551, 1558100] C671 139) [15581, 7102, 6377201] C671
91) [3581, 301, 14593] C671 136) [14593, 602, 32229] C671
92) [3581, 5926, 6716713] C671 129) [12697, 2963, 515664] C671
93) [3581, 5502, 7338817] C671 132) [13873, 2751, 57296] C671
94) [3593, 330, 12853] C671 131) [12853, 165, 3593] C671
95) [3697, 3571, 2780416] C671 123) [10861, 6001, 181153] C671
96) [3769, 4550, 1316169] C671 141) [16249, 2275, 964864] C671
97) [3917, 2617, 771113] C671 ---) [15737, 5234, 3764237] C2013
98) [3929, 5695, 3431764] C671 145) [17509, 7041, 98225] C671
99) [4021, 4986, 408725] C671 142) [16349, 2493, 1451581] C671
100) [4057, 1947, 313796] C671 ---) [1601, 2567, 1038592] C4697
101) [4073, 3698, 2099149] C671 126) [12421, 1849, 329913] C671
102) [4093, 5721, 7542929] C671 120) [8969, 3279, 802228] C671
103) [4241, 5951, 1897300] C671 147) [18973, 7097, 4618449] C671
104) [4273, 5619, 175184] C671 ---) [10949, 4281, 3593593] C2013
105) [4349, 2369, 219025] C671 ---) [8761, 4738, 4736061] C18117
106) [4421, 1417, 14557] C671 134) [14557, 2834, 1949661] C671
107) [4549, 7334, 1146393] C671 133) [14153, 3667, 3075124] C671
108) [4909, 5758, 8210097] C671 146) [18617, 2879, 19636] C671
109) [5077, 7038, 4260161] C671 124) [11801, 3519, 2030800] C671
110) [5237, 7445, 1538273] C671 130) [12713, 4483, 4105808] C671
111) [5237, 6801, 2104069] C671 144) [17389, 9957, 12574037] C671
112) [5393, 4011, 3794176] C671 138) [14821, 8022, 911417] C671
113) [5569, 7282, 11452525] C671 121) [9349, 3641, 451089] C671
114) [5689, 3783, 948032] C671 137) [14813, 7566, 10518961] C671
115) [5693, 3045, 2145793] C671 128) [12697, 6090, 688853] C671
116) [5981, 477, 19501] C671 148) [19501, 954, 149525] C671
117) [5981, 9937, 15354137] C671 ---) [18257, 7147, 12655796] C2013
118) [6529, 1807, 344592] C671 79) [2393, 3614, 1886881] C671
119) [8089, 519, 16784] C671 70) [1049, 1038, 202225] C671
120) [8969, 3279, 802228] C671 102) [4093, 5721, 7542929] C671
121) [9349, 3641, 451089] C671 113) [5569, 7282, 11452525] C671
122) [10369, 3090, 2345549] C671 83) [2789, 1545, 10369] C671
123) [10861, 6001, 181153] C671 95) [3697, 3571, 2780416] C671
124) [11801, 3519, 2030800] C671 109) [5077, 7038, 4260161] C671
125) [12281, 1679, 628004] C671 ---) [929, 3358, 307025] C61
126) [12421, 1849, 329913] C671 101) [4073, 3698, 2099149] C671
127) [12473, 163, 3524] C671 67) [881, 326, 12473] C671
128) [12697, 6090, 688853] C671 115) [5693, 3045, 2145793] C671
129) [12697, 2963, 515664] C671 92) [3581, 5926, 6716713] C671
130) [12713, 4483, 4105808] C671 110) [5237, 7445, 1538273] C671
131) [12853, 165, 3593] C671 94) [3593, 330, 12853] C671
132) [13873, 2751, 57296] C671 93) [3581, 5502, 7338817] C671
133) [14153, 3667, 3075124] C671 107) [4549, 7334, 1146393] C671
134) [14557, 2834, 1949661] C671 106) [4421, 1417, 14557] C671
135) [14557, 1642, 149989] C671 88) [3061, 821, 131013] C671
136) [14593, 602, 32229] C671 91) [3581, 301, 14593] C671
137) [14813, 7566, 10518961] C671 114) [5689, 3783, 948032] C671
138) [14821, 8022, 911417] C671 112) [5393, 4011, 3794176] C671
139) [15581, 7102, 6377201] C671 90) [3449, 3551, 1558100] C671
140) [15581, 6633, 8564641] C671 87) [3049, 3755, 2243664] C671
141) [16249, 2275, 964864] C671 96) [3769, 4550, 1316169] C671
142) [16349, 2493, 1451581] C671 99) [4021, 4986, 408725] C671
143) [16573, 5553, 7704809] C671 89) [3209, 5163, 1657300] C671
144) [17389, 9957, 12574037] C671 111) [5237, 6801, 2104069] C671
145) [17509, 7041, 98225] C671 98) [3929, 5695, 3431764] C671
146) [18617, 2879, 19636] C671 108) [4909, 5758, 8210097] C671
147) [18973, 7097, 4618449] C671 103) [4241, 5951, 1897300] C671
148) [19501, 954, 149525] C671 116) [5981, 477, 19501] C671
149) [20369, 826, 89093] C671 ---) [53, 413, 20369] C61
150) [26561, 255, 9616] C671 63) [601, 510, 26561] C671
151) [42841, 1939, 72400] C671 52) [181, 2089, 1071025] C671
152) [67157, 277, 2393] C671 80) [2393, 554, 67157] C671
153) [67273, 283, 3204] C671 42) [89, 566, 67273] C671
154) [74101, 1250, 94221] C671 ---) [29, 625, 74101] C61
155) [81677, 305, 2837] C671 84) [2837, 610, 81677] C671
156) [88241, 327, 4672] C671 38) [73, 654, 88241] C671
157) [105253, 437, 21429] C671 78) [2381, 874, 105253] C671
158) [137777, 775, 115712] C671 50) [113, 1550, 137777] C671
159) [148861, 1562, 14517] C671 73) [1613, 781, 148861] C671
160) [169657, 419, 1476] C671 33) [41, 838, 169657] C671
161) [170509, 529, 27333] C671 85) [3037, 1058, 170509] C671
162) [174737, 983, 197888] C671 65) [773, 1966, 174737] C671
163) [194917, 2186, 414981] C671 69) [941, 1093, 194917] C671
164) [221813, 701, 67397] C671 62) [557, 1402, 221813] C671
165) [285557, 645, 32617] C671 53) [193, 1290, 285557] C671
166) [313829, 2258, 19325] C671 66) [773, 1129, 313829] C671
167) [326449, 2947, 130896] C671 45) [101, 5721, 8161225] C671
168) [352601, 595, 356] C671 41) [89, 1190, 352601] C671
169) [415801, 2699, 1717200] C671 35) [53, 4089, 415801] C671
170) [482441, 707, 4352] C671 ---) [17, 1414, 482441] C61
171) [574801, 1751, 622800] C671 51) [173, 3502, 574801] C671
172) [645581, 809, 2225] C671 43) [89, 1618, 645581] C671
173) [736433, 1991, 806912] C671 54) [197, 3982, 736433] C671
174) [754577, 1367, 278528] C671 28) [17, 2734, 754577] C671
175) [880409, 947, 4100] C671 32) [41, 1894, 880409] C671
176) [1180241, 1271, 108800] C671 27) [17, 2542, 1180241] C671
177) [1724153, 1323, 6544] C671 61) [409, 2646, 1724153] C671
178) [1748833, 1615, 214848] C671 59) [373, 3230, 1748833] C671
179) [3816881, 1959, 5200] C671 25) [13, 3918, 3816881] C671
180) [4349489, 2311, 247808] C671 21) [8, 4622, 4349489] C671
181) [4711537, 2215, 48672] C671 23) [8, 4430, 4711537] C671
182) [5160041, 2579, 372800] C671 55) [233, 5158, 5160041] C671
183) [5200177, 2311, 35136] C671 37) [61, 4622, 5200177] C671
184) [5652833, 2511, 163072] C671 26) [13, 5022, 5652833] C671
185) [5660393, 2515, 166208] C671 36) [53, 5030, 5660393] C671
186) [6980777, 2643, 1168] C671 39) [73, 5286, 6980777] C671
187) [7482577, 2743, 10368] C671 22) [8, 5486, 7482577] C671
188) [7485721, 2939, 288000] C671 5) [5, 5878, 7485721] C671
189) [7702889, 3091, 462848] C671 47) [113, 6182, 7702889] C671
190) [7838321, 2983, 264992] C671 20) [8, 5966, 7838321] C671
191) [8220929, 2879, 16928] C671 19) [8, 5758, 8220929] C671
192) [9689521, 3751, 1095120] C671 13) [5, 6573, 9689521] C671
193) [10086617, 3867, 1216768] C671 44) [97, 7734, 10086617] C671
194) [10175057, 3191, 1856] C671 29) [29, 6382, 10175057] C671
195) [10598537, 3267, 18688] C671 40) [73, 6534, 10598537] C671
196) [11080841, 3779, 800000] C671 12) [5, 7337, 11080841] C671
197) [11579209, 3523, 208080] C671 3) [5, 7046, 11579209] C671
198) [12383249, 3607, 156800] C671 14) [8, 7214, 12383249] C671
199) [12837641, 3587, 7232] C671 48) [113, 7174, 12837641] C671
200) [15497177, 3995, 115712] C671 49) [113, 7990, 15497177] C671
201) [16680793, 4187, 212544] C671 31) [41, 8374, 16680793] C671
202) [19124929, 4607, 524880] C671 10) [5, 9214, 19124929] C671
203) [19345873, 4759, 825552] C671 24) [13, 9518, 19345873] C671
204) [20346889, 4763, 584820] C671 2) [5, 9526, 20346889] C671
205) [20966921, 4579, 80] C671 11) [5, 9158, 20966921] C671
206) [21483169, 4783, 348480] C671 8) [5, 9566, 21483169] C671
207) [27686569, 5587, 882000] C671 4) [5, 11174, 27686569] C671
208) [34953929, 5923, 32000] C671 7) [5, 11846, 34953929] C671