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 C3 x C117 non-normal (D4) quartic CM field invariants: 188 fields

K Quartic invariants Cl(OK) Igusa invariants Kr Reflex invariants Cl(OKr) Igusa invariants
1) [5, 6641, 9381209] C3 x C117 ---) [9381209, 3547, 800000] C3 x C3 x C819
2) [5, 7894, 15570809] C3 x C117 188) [15570809, 3947, 2000] C3 x C117
3) [5, 3278, 2679841] C3 x C117 ---) [2679841, 1639, 1620] C39 x C117
4) [5, 4342, 4650521] C3 x C117 185) [4650521, 2171, 15680] C3 x C117
5) [5, 6814, 11095649] C3 x C117 187) [11095649, 3407, 128000] C3 x C117
6) [8, 2010, 612193] C3 x C117 162) [612193, 1005, 99458] C3 x C117
7) [8, 8902, 19350601] C3 x C117 ---) [19350601, 4451, 115200] C3 x C3 x C117
8) [8, 8774, 19245257] C3 x C117 ---) [19245257, 4387, 128] C3 x C2223
9) [13, 6561, 6677597] C3 x C117 186) [6677597, 7113, 10979293] C3 x C117
10) [17, 2530, 1588733] C3 x C117 173) [1588733, 1265, 2873] C3 x C117
11) [29, 1846, 513673] C3 x C117 159) [513673, 923, 84564] C3 x C117
12) [37, 3374, 2760721] C3 x C117 179) [2760721, 1687, 21312] C3 x C117
13) [37, 7582, 14085153] C3 x C117 ---) [1565017, 3791, 71632] C3 x C3 x C117
14) [41, 2074, 850853] C3 x C117 166) [850853, 1037, 56129] C3 x C117
15) [41, 8870, 19627241] C3 x C117 ---) [19627241, 4435, 10496] C3 x C3 x C117
16) [41, 1875, 472996] C3 x C117 138) [118249, 1951, 212544] C3 x C117
17) [53, 1582, 434881] C3 x C117 157) [434881, 791, 47700] C3 x C117
18) [61, 2990, 2226241] C3 x C117 175) [2226241, 1495, 2196] C3 x C117
19) [73, 4086, 3258137] C3 x C117 181) [3258137, 2043, 228928] C3 x C117
20) [229, 962, 25261] C3 x C117 ---) [25261, 481, 51525] C117
21) [229, 529, 28225] C3 x C117 ---) [1129, 319, 22900] C9 x C117
22) [229, 594, 65309] C3 x C117 130) [65309, 297, 5725] C3 x C117
23) [257, 2303, 1325888] C3 x C117 ---) [20717, 2153, 1153673] C117
24) [257, 886, 130457] C3 x C117 ---) [130457, 443, 16448] C819
25) [277, 1241, 376641] C3 x C117 124) [41849, 2482, 33517] C3 x C117
26) [317, 1586, 566717] C3 x C117 160) [566717, 793, 15533] C3 x C117
27) [433, 2262, 586361] C3 x C117 161) [586361, 1131, 173200] C3 x C117
28) [661, 1049, 273613] C3 x C117 150) [273613, 2098, 5949] C3 x C117
29) [709, 2309, 1332693] C3 x C117 104) [16453, 3157, 1566181] C3 x C117
30) [761, 607, 8212] C3 x C117 ---) [2053, 1214, 335601] C117
31) [761, 2323, 1294100] C3 x C117 ---) [12941, 2245, 92081] C117
32) [761, 162, 3517] C3 x C117 ---) [3517, 81, 761] C117
33) [761, 1467, 81232] C3 x C117 ---) [5077, 1789, 6849] C117
34) [761, 178, 4877] C3 x C117 ---) [4877, 89, 761] C117
35) [761, 1195, 149824] C3 x C117 ---) [2341, 829, 171225] C117
36) [941, 2278, 1056425] C3 x C117 125) [42257, 1139, 60224] C3 x C117
37) [1049, 862, 168977] C3 x C117 145) [168977, 431, 4196] C3 x C117
38) [1129, 398, 21537] C3 x C117 ---) [2393, 199, 4516] C39
39) [1153, 4562, 1324269] C3 x C117 103) [16349, 2281, 969673] C3 x C117
40) [1193, 1438, 497873] C3 x C117 158) [497873, 719, 4772] C3 x C117
41) [1229, 1258, 390725] C3 x C117 ---) [15629, 629, 1229] C9 x C117
42) [1229, 1037, 157925] C3 x C117 ---) [6317, 2074, 443669] C117
43) [1373, 1517, 517313] C3 x C117 ---) [1433, 875, 87872] C117
44) [1409, 2739, 1393300] C3 x C117 96) [13933, 3801, 2605241] C3 x C117
45) [1901, 601, 89825] C3 x C117 ---) [3593, 1202, 1901] C117
46) [1901, 1269, 390709] C3 x C117 62) [3229, 2445, 1901] C3 x C117
47) [1997, 398, 7649] C3 x C117 86) [7649, 199, 7988] C3 x C117
48) [2089, 2307, 176912] C3 x C117 92) [11057, 4614, 4614601] C3 x C117
49) [2137, 4671, 3594836] C3 x C117 109) [18341, 4493, 53425] C3 x C117
50) [2273, 1543, 549184] C3 x C117 ---) [8581, 3086, 184113] C3 x C3 x C117
51) [2341, 2665, 131589] C3 x C117 98) [14621, 5330, 6575869] C3 x C117
52) [2389, 4401, 4339913] C3 x C117 99) [15017, 4519, 3449716] C3 x C117
53) [2437, 330, 17477] C3 x C117 ---) [17477, 165, 2437] C3 x C3 x C117
54) [2777, 1939, 572672] C3 x C117 ---) [2237, 2341, 336017] C117
55) [2777, 422, 89] C3 x C117 ---) [89, 211, 11108] C117
56) [2837, 293, 20753] C3 x C117 112) [20753, 586, 2837] C3 x C117
57) [2837, 1777, 771701] C3 x C117 102) [15749, 3554, 70925] C3 x C117
58) [2861, 3985, 1131229] C3 x C117 89) [9349, 4965, 3916709] C3 x C117
59) [2917, 1121, 190917] C3 x C117 ---) [2357, 2242, 492973] C117
60) [2917, 550, 28953] C3 x C117 ---) [3217, 275, 11668] C117
61) [3221, 2733, 88525] C3 x C117 ---) [3541, 2645, 260901] C117
62) [3229, 2445, 1901] C3 x C117 46) [1901, 1269, 390709] C3 x C117
63) [3413, 2381, 884009] C3 x C117 108) [18041, 4762, 2133125] C3 x C117
64) [3533, 4838, 5625449] C3 x C117 84) [6689, 2419, 56528] C3 x C117
65) [3637, 2129, 1110429] C3 x C117 95) [13709, 4258, 90925] C3 x C117
66) [3889, 1710, 668801] C3 x C117 ---) [13649, 855, 15556] C117
67) [4481, 2651, 940288] C3 x C117 ---) [3673, 3311, 161316] C117
68) [4597, 629, 5821] C3 x C117 79) [5821, 1258, 372357] C3 x C117
69) [4649, 4315, 878656] C3 x C117 ---) [13729, 7659, 14579264] C117
70) [4649, 590, 12641] C3 x C117 ---) [12641, 295, 18596] C117
71) [5081, 1947, 946432] C3 x C117 ---) [3697, 3894, 5081] C117
72) [5113, 5015, 201808] C3 x C117 93) [12613, 6869, 6999697] C3 x C117
73) [5281, 6019, 1229328] C3 x C117 ---) [8537, 3807, 3569956] C117
74) [5309, 5993, 270925] C3 x C117 91) [10837, 7097, 430029] C3 x C117
75) [5413, 7913, 160533] C3 x C117 107) [17837, 6105, 9099253] C3 x C117
76) [5653, 5794, 7827309] C3 x C117 106) [17749, 2897, 141325] C3 x C117
77) [5749, 7549, 1275669] C3 x C117 101) [15749, 6249, 9664069] C3 x C117
78) [5813, 9914, 22688437] C3 x C117 105) [16573, 4957, 470853] C3 x C117
79) [5821, 1258, 372357] C3 x C117 68) [4597, 629, 5821] C3 x C117
80) [6053, 322, 1709] C3 x C117 ---) [1709, 161, 6053] C117
81) [6133, 669, 110357] C3 x C117 ---) [653, 1338, 6133] C117
82) [6133, 3149, 809341] C3 x C117 ---) [4789, 4769, 5157853] C117
83) [6637, 3733, 1212309] C3 x C117 ---) [2749, 2993, 6637] C117
84) [6689, 2419, 56528] C3 x C117 64) [3533, 4838, 5625449] C3 x C117
85) [7537, 715, 110848] C3 x C117 ---) [433, 1430, 67833] C117
86) [7649, 199, 7988] C3 x C117 47) [1997, 398, 7649] C3 x C117
87) [7873, 2951, 1734244] C3 x C117 ---) [1201, 2267, 503872] C39
88) [8581, 281, 433] C3 x C117 ---) [433, 562, 77229] C117
89) [9349, 4965, 3916709] C3 x C117 58) [2861, 3985, 1131229] C3 x C117
90) [9749, 1230, 222241] C3 x C117 ---) [769, 615, 38996] C117
91) [10837, 7097, 430029] C3 x C117 74) [5309, 5993, 270925] C3 x C117
92) [11057, 4614, 4614601] C3 x C117 48) [2089, 2307, 176912] C3 x C117
93) [12613, 6869, 6999697] C3 x C117 72) [5113, 5015, 201808] C3 x C117
94) [13033, 595, 85248] C3 x C117 ---) [37, 685, 117297] C3 x C9
95) [13709, 4258, 90925] C3 x C117 65) [3637, 2129, 1110429] C3 x C117
96) [13933, 3801, 2605241] C3 x C117 44) [1409, 2739, 1393300] C3 x C117
97) [14321, 223, 8852] C3 x C117 ---) [2213, 446, 14321] C3 x C3 x C117
98) [14621, 5330, 6575869] C3 x C117 51) [2341, 2665, 131589] C3 x C117
99) [15017, 4519, 3449716] C3 x C117 52) [2389, 4401, 4339913] C3 x C117
100) [15629, 937, 28037] C3 x C117 ---) [53, 497, 15629] C39
101) [15749, 6249, 9664069] C3 x C117 77) [5749, 7549, 1275669] C3 x C117
102) [15749, 3554, 70925] C3 x C117 57) [2837, 1777, 771701] C3 x C117
103) [16349, 2281, 969673] C3 x C117 39) [1153, 4562, 1324269] C3 x C117
104) [16453, 3157, 1566181] C3 x C117 29) [709, 2309, 1332693] C3 x C117
105) [16573, 4957, 470853] C3 x C117 78) [5813, 9914, 22688437] C3 x C117
106) [17749, 2897, 141325] C3 x C117 76) [5653, 5794, 7827309] C3 x C117
107) [17837, 6105, 9099253] C3 x C117 75) [5413, 7913, 160533] C3 x C117
108) [18041, 4762, 2133125] C3 x C117 63) [3413, 2381, 884009] C3 x C117
109) [18341, 4493, 53425] C3 x C117 49) [2137, 4671, 3594836] C3 x C117
110) [18541, 10685, 16486021] C3 x C117 ---) [5869, 6353, 463525] C117
111) [20353, 547, 29008] C3 x C117 ---) [37, 733, 20353] C117
112) [20753, 586, 2837] C3 x C117 56) [2837, 293, 20753] C3 x C117
113) [22229, 205, 4949] C3 x C117 ---) [101, 410, 22229] C117
114) [22769, 159, 628] C3 x C117 ---) [157, 318, 22769] C117
115) [23689, 823, 116032] C3 x C117 ---) [37, 709, 23689] C117
116) [24029, 209, 4913] C3 x C117 ---) [17, 418, 24029] C39
117) [25301, 953, 68921] C3 x C117 ---) [41, 935, 101204] C117
118) [25981, 1209, 358925] C3 x C117 ---) [293, 2418, 25981] C117
119) [25981, 485, 349] C3 x C117 ---) [349, 970, 233829] C117
120) [28837, 1430, 49833] C3 x C117 ---) [113, 715, 115348] C117
121) [33457, 807, 154448] C3 x C117 ---) [197, 1614, 33457] C117
122) [34877, 1614, 93217] C3 x C117 ---) [97, 807, 139508] C117
123) [36653, 409, 32657] C3 x C117 ---) [113, 818, 36653] C117
124) [41849, 2482, 33517] C3 x C117 25) [277, 1241, 376641] C3 x C117
125) [42257, 1139, 60224] C3 x C117 36) [941, 2278, 1056425] C3 x C117
126) [48481, 391, 26100] C3 x C117 ---) [29, 782, 48481] C117
127) [54181, 1122, 97997] C3 x C117 ---) [53, 561, 54181] C117
128) [58049, 543, 59200] C3 x C117 ---) [37, 1086, 58049] C117
129) [59809, 1975, 242496] C3 x C117 ---) [421, 3950, 2930641] C117
130) [65309, 297, 5725] C3 x C117 22) [229, 594, 65309] C3 x C117
131) [75821, 1106, 2525] C3 x C117 ---) [101, 553, 75821] C117
132) [89069, 1202, 4925] C3 x C117 ---) [197, 601, 89069] C117
133) [92581, 309, 725] C3 x C117 ---) [29, 618, 92581] C117
134) [95621, 437, 23837] C3 x C117 ---) [197, 874, 95621] C117
135) [97021, 1490, 166941] C3 x C117 ---) [229, 745, 97021] C3 x C3 x C117
136) [111409, 1362, 18125] C3 x C117 ---) [29, 681, 111409] C117
137) [118033, 391, 8712] C3 x C117 ---) [8, 782, 118033] C117
138) [118249, 1951, 212544] C3 x C117 16) [41, 1875, 472996] C3 x C117
139) [119129, 827, 141200] C3 x C117 ---) [353, 1654, 119129] C117
140) [122273, 365, 2738] C3 x C117 ---) [8, 730, 122273] C117
141) [130369, 381, 3698] C3 x C117 ---) [8, 762, 130369] C117
142) [146161, 415, 6516] C3 x C117 ---) [181, 830, 146161] C117
143) [152017, 423, 6728] C3 x C117 ---) [8, 846, 152017] C117
144) [167633, 439, 6272] C3 x C117 ---) [8, 878, 167633] C117
145) [168977, 431, 4196] C3 x C117 37) [1049, 862, 168977] C3 x C117
146) [170249, 1271, 20800] C3 x C117 ---) [13, 873, 170249] C117
147) [174049, 2347, 289296] C3 x C117 ---) [41, 2247, 696196] C117
148) [194269, 457, 3645] C3 x C117 ---) [5, 914, 194269] C39
149) [266081, 719, 62720] C3 x C117 ---) [5, 1037, 266081] C117
150) [273613, 2098, 5949] C3 x C117 28) [661, 1049, 273613] C3 x C117
151) [288481, 655, 35136] C3 x C117 ---) [61, 1310, 288481] C117
152) [318377, 627, 18688] C3 x C117 ---) [73, 1254, 318377] C117
153) [326681, 891, 116800] C3 x C117 ---) [73, 1782, 326681] C117
154) [374669, 1837, 637] C3 x C117 ---) [13, 1449, 374669] C117
155) [376853, 621, 2197] C3 x C117 ---) [13, 1242, 376853] C117
156) [386437, 2602, 146853] C3 x C117 ---) [37, 1301, 386437] C117
157) [434881, 791, 47700] C3 x C117 17) [53, 1582, 434881] C3 x C117
158) [497873, 719, 4772] C3 x C117 40) [1193, 1438, 497873] C3 x C117
159) [513673, 923, 84564] C3 x C117 11) [29, 1846, 513673] C3 x C117
160) [566717, 793, 15533] C3 x C117 26) [317, 1586, 566717] C3 x C117
161) [586361, 1131, 173200] C3 x C117 27) [433, 2262, 586361] C3 x C117
162) [612193, 1005, 99458] C3 x C117 6) [8, 2010, 612193] C3 x C117
163) [651401, 899, 39200] C3 x C117 ---) [8, 1798, 651401] C117
164) [671921, 839, 8000] C3 x C117 ---) [5, 1678, 671921] C117
165) [694541, 961, 57245] C3 x C117 ---) [5, 1813, 694541] C117
166) [850853, 1037, 56129] C3 x C117 14) [41, 2074, 850853] C3 x C117
167) [878929, 1399, 269568] C3 x C117 ---) [13, 2798, 878929] C117
168) [891049, 979, 16848] C3 x C117 ---) [13, 1958, 891049] C117
169) [893929, 947, 720] C3 x C117 ---) [5, 1894, 893929] C117
170) [1179569, 1087, 500] C3 x C117 ---) [5, 2174, 1179569] C117
171) [1413221, 1189, 125] C3 x C117 ---) [5, 2378, 1413221] C117
172) [1531129, 1739, 373248] C3 x C117 ---) [8, 3478, 1531129] C117
173) [1588733, 1265, 2873] C3 x C117 10) [17, 2530, 1588733] C3 x C117
174) [1803541, 1357, 9477] C3 x C117 ---) [13, 2714, 1803541] C117
175) [2226241, 1495, 2196] C3 x C117 18) [61, 2990, 2226241] C3 x C117
176) [2269961, 1507, 272] C3 x C117 ---) [17, 3014, 2269961] C117
177) [2325881, 2315, 758336] C3 x C117 ---) [41, 4630, 2325881] C117
178) [2396057, 1595, 36992] C3 x C117 ---) [8, 3190, 2396057] C117
179) [2760721, 1687, 21312] C3 x C117 12) [37, 3374, 2760721] C3 x C117
180) [3202169, 1931, 131648] C3 x C117 ---) [17, 3862, 3202169] C117
181) [3258137, 2043, 228928] C3 x C117 19) [73, 4086, 3258137] C3 x C117
182) [3267289, 1819, 10368] C3 x C117 ---) [8, 3638, 3267289] C117
183) [3607229, 3097, 1496045] C3 x C117 ---) [5, 3821, 3607229] C117
184) [4513577, 2995, 1114112] C3 x C117 ---) [17, 5990, 4513577] C117
185) [4650521, 2171, 15680] C3 x C117 4) [5, 4342, 4650521] C3 x C117
186) [6677597, 7113, 10979293] C3 x C117 9) [13, 6561, 6677597] C3 x C117
187) [11095649, 3407, 128000] C3 x C117 5) [5, 6814, 11095649] C3 x C117
188) [15570809, 3947, 2000] C3 x C117 2) [5, 7894, 15570809] C3 x C117