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 C189 non-normal (D4) quartic CM field invariants: 156 fields

K Quartic invariants Cl(OK) Igusa invariants Kr Reflex invariants Cl(OKr) Igusa invariants
1) [5, 5318, 6450761] C3 x C189 ---) [6450761, 2659, 154880] C3 x C945
2) [5, 5038, 5780881] C3 x C189 151) [5780881, 2519, 141120] C3 x C189
3) [8, 9826, 24065369] C3 x C189 156) [24065369, 4913, 18050] C3 x C189
4) [13, 5022, 4225121] C3 x C189 147) [4225121, 2511, 520000] C3 x C189
5) [13, 3513, 3001049] C3 x C189 142) [3001049, 6671, 4373200] C3 x C189
6) [13, 7929, 14138381] C3 x C189 155) [14138381, 15009, 52782925] C3 x C189
7) [37, 4374, 2358137] C3 x C189 ---) [2358137, 2187, 606208] C3 x C4725
8) [61, 3677, 3340417] C3 x C189 ---) [3340417, 7354, 158661] C3 x C3 x C189
9) [61, 2350, 669121] C3 x C189 129) [669121, 1175, 177876] C3 x C189
10) [89, 1402, 482501] C3 x C189 126) [482501, 701, 2225] C3 x C189
11) [89, 6118, 8992937] C3 x C189 153) [8992937, 3059, 91136] C3 x C189
12) [109, 1590, 630281] C3 x C189 128) [630281, 795, 436] C3 x C189
13) [113, 5830, 8236873] C3 x C189 ---) [8236873, 2915, 65088] C3 x C3 x C189
14) [137, 4726, 5268121] C3 x C189 ---) [5268121, 2363, 78912] C3 x C3 x C189
15) [229, 609, 72053] C3 x C189 ---) [72053, 1218, 82669] C189
16) [229, 645, 73721] C3 x C189 ---) [73721, 1290, 121141] C189
17) [229, 2249, 282033] C3 x C189 ---) [31337, 1599, 443344] C189
18) [257, 338, 19309] C3 x C189 ---) [19309, 169, 2313] C189
19) [257, 2038, 775193] C3 x C189 ---) [775193, 1019, 65792] C189
20) [313, 2182, 1185273] C3 x C189 88) [14633, 1091, 1252] C3 x C189
21) [521, 1727, 688192] C3 x C189 81) [10753, 2163, 1102436] C3 x C189
22) [733, 881, 17937] C3 x C189 ---) [1993, 955, 187648] C189
23) [733, 1745, 33937] C3 x C189 ---) [33937, 3490, 2909277] C189
24) [733, 1605, 6113] C3 x C189 ---) [6113, 2155, 46912] C945
25) [1009, 2995, 2211984] C3 x C189 ---) [15361, 3047, 1456996] C3 x C27
26) [1153, 4211, 72196] C3 x C189 96) [18049, 3923, 558052] C3 x C189
27) [1373, 1869, 749377] C3 x C189 ---) [2593, 1051, 197712] C189
28) [1637, 790, 51257] C3 x C189 ---) [51257, 395, 26192] C3 x C3 x C945
29) [1949, 1505, 308501] C3 x C189 121) [308501, 3010, 1031021] C3 x C189
30) [2213, 1741, 155281] C3 x C189 ---) [3169, 2019, 885200] C189
31) [2213, 373, 7673] C3 x C189 73) [7673, 746, 108437] C3 x C189
32) [2237, 1209, 15889] C3 x C189 ---) [15889, 2418, 1398125] C3 x C945
33) [2557, 573, 4733] C3 x C189 ---) [4733, 1146, 309397] C189
34) [2557, 4310, 1330153] C3 x C189 ---) [10993, 2155, 828468] C189
35) [2633, 1938, 675661] C3 x C189 87) [13789, 969, 65825] C3 x C189
36) [2677, 4401, 6869] C3 x C189 ---) [6869, 2361, 773653] C189
37) [2677, 4514, 4997677] C3 x C189 ---) [17293, 2257, 24093] C189
38) [2677, 2865, 1489217] C3 x C189 ---) [5153, 2583, 1295668] C189
39) [2713, 2195, 465892] C3 x C189 ---) [2377, 1523, 531748] C189
40) [2801, 1247, 332032] C3 x C189 ---) [1297, 1563, 11204] C3 x C2079
41) [2861, 1201, 199669] C3 x C189 120) [199669, 2402, 643725] C3 x C189
42) [3221, 1365, 465001] C3 x C189 ---) [1609, 2479, 1043604] C189
43) [3221, 929, 118325] C3 x C189 ---) [4733, 1858, 389741] C189
44) [3221, 2861, 112925] C3 x C189 ---) [4517, 2753, 1703909] C189
45) [3413, 5205, 2226037] C3 x C189 100) [18397, 8373, 412973] C3 x C189
46) [3677, 2173, 1025129] C3 x C189 104) [20921, 4346, 621413] C3 x C189
47) [3797, 874, 54277] C3 x C189 111) [54277, 437, 34173] C3 x C189
48) [3797, 8054, 5949641] C3 x C189 ---) [16481, 4027, 2566772] C3 x C3 x C189
49) [3853, 982, 179433] C3 x C189 103) [19937, 491, 15412] C3 x C189
50) [4013, 7725, 6610993] C3 x C189 99) [18313, 6603, 786548] C3 x C189
51) [4093, 4781, 1121121] C3 x C189 ---) [13841, 7899, 65488] C3 x C945
52) [4481, 5619, 175888] C3 x C189 ---) [10993, 6419, 2581056] C189
53) [4481, 1202, 343277] C3 x C189 ---) [2837, 601, 4481] C189
54) [4597, 2149, 50121] C3 x C189 ---) [5569, 4298, 4417717] C189
55) [4933, 3106, 24237] C3 x C189 ---) [2693, 1553, 596893] C189
56) [4933, 3374, 4561] C3 x C189 ---) [4561, 1687, 710352] C189
57) [4933, 1537, 441369] C3 x C189 ---) [5449, 3074, 596893] C189
58) [5261, 1197, 135925] C3 x C189 ---) [5437, 2394, 889109] C189
59) [5261, 1606, 560633] C3 x C189 ---) [1553, 803, 21044] C189
60) [5297, 1019, 35792] C3 x C189 ---) [2237, 2038, 895193] C189
61) [5297, 5227, 885824] C3 x C189 ---) [13841, 7279, 13242500] C945
62) [5333, 338, 7229] C3 x C189 ---) [7229, 169, 5333] C945
63) [5333, 2310, 992713] C3 x C189 ---) [1033, 1155, 85328] C189
64) [5557, 630, 10313] C3 x C189 ---) [10313, 315, 22228] C21 x C189
65) [5741, 4202, 2554117] C3 x C189 ---) [3037, 2101, 465021] C189
66) [5749, 6389, 775033] C3 x C189 92) [15817, 10259, 367936] C3 x C189
67) [5821, 1621, 480825] C3 x C189 ---) [2137, 3242, 704341] C189
68) [5869, 4961, 2911725] C3 x C189 86) [12941, 8489, 17753725] C3 x C189
69) [5981, 8942, 8410625] C3 x C189 ---) [13457, 4471, 2894804] C3 x C2457
70) [6053, 409, 3989] C3 x C189 ---) [3989, 818, 151325] C189
71) [6053, 2509, 1499621] C3 x C189 ---) [5189, 5018, 296597] C189
72) [6997, 985, 30897] C3 x C189 ---) [3433, 1970, 846637] C189
73) [7673, 746, 108437] C3 x C189 31) [2213, 373, 7673] C3 x C189
74) [7753, 586, 54837] C3 x C189 ---) [677, 293, 7753] C189
75) [9133, 4677, 1246853] C3 x C189 ---) [2357, 2489, 1543477] C189
76) [9293, 4045, 3697877] C3 x C189 ---) [4397, 5101, 1570517] C189
77) [9293, 2665, 546557] C3 x C189 ---) [4517, 5330, 4915997] C189
78) [9749, 493, 58325] C3 x C189 ---) [2333, 986, 9749] C189
79) [10301, 1758, 113377] C3 x C189 ---) [937, 879, 164816] C189
80) [10357, 1010, 213597] C3 x C189 ---) [293, 505, 10357] C3 x C27
81) [10753, 2163, 1102436] C3 x C189 21) [521, 1727, 688192] C3 x C189
82) [10889, 1347, 320212] C3 x C189 ---) [277, 1461, 533561] C189
83) [10949, 985, 217921] C3 x C189 ---) [1801, 1970, 98541] C189
84) [11777, 2167, 1171028] C3 x C189 ---) [1013, 3425, 1990313] C189
85) [12577, 2383, 1416528] C3 x C189 ---) [1093, 2885, 12577] C945
86) [12941, 8489, 17753725] C3 x C189 68) [5869, 4961, 2911725] C3 x C189
87) [13789, 969, 65825] C3 x C189 35) [2633, 1938, 675661] C3 x C189
88) [14633, 1091, 1252] C3 x C189 20) [313, 2182, 1185273] C3 x C189
89) [15641, 147, 1492] C3 x C189 ---) [373, 294, 15641] C189
90) [15733, 3165, 2500373] C3 x C189 ---) [557, 1921, 770917] C189
91) [15737, 2695, 1150868] C3 x C189 ---) [797, 3377, 2659553] C189
92) [15817, 10259, 367936] C3 x C189 66) [5749, 6389, 775033] C3 x C189
93) [16661, 3061, 139013] C3 x C189 ---) [2837, 6122, 8813669] C189
94) [17477, 149, 1181] C3 x C189 ---) [1181, 298, 17477] C189
95) [17581, 421, 4753] C3 x C189 ---) [97, 842, 158229] C189
96) [18049, 3923, 558052] C3 x C189 26) [1153, 4211, 72196] C3 x C189
97) [18097, 4334, 4406337] C3 x C189 ---) [2897, 2167, 72388] C189
98) [18257, 2483, 1500244] C3 x C189 ---) [709, 2829, 894593] C189
99) [18313, 6603, 786548] C3 x C189 50) [4013, 7725, 6610993] C3 x C189
100) [18397, 8373, 412973] C3 x C189 45) [3413, 5205, 2226037] C3 x C189
101) [18661, 2490, 1475381] C3 x C189 ---) [2789, 1245, 18661] C189
102) [18701, 3085, 1813601] C3 x C189 ---) [521, 2191, 1196864] C189
103) [19937, 491, 15412] C3 x C189 49) [3853, 982, 179433] C3 x C189
104) [20921, 4346, 621413] C3 x C189 46) [3677, 2173, 1025129] C3 x C189
105) [22397, 1646, 318977] C3 x C189 ---) [233, 823, 89588] C189
106) [25793, 1175, 338708] C3 x C189 ---) [293, 2350, 25793] C189
107) [43717, 2230, 543753] C3 x C189 ---) [137, 1115, 174868] C189
108) [44273, 890, 20933] C3 x C189 ---) [173, 445, 44273] C189
109) [45433, 267, 6464] C3 x C189 ---) [101, 534, 45433] C189
110) [47701, 2157, 578825] C3 x C189 ---) [137, 1527, 190804] C189
111) [54277, 437, 34173] C3 x C189 47) [3797, 874, 54277] C3 x C189
112) [56489, 371, 20288] C3 x C189 ---) [317, 742, 56489] C189
113) [69401, 3487, 107600] C3 x C189 ---) [269, 2677, 1735025] C189
114) [92857, 331, 4176] C3 x C189 ---) [29, 662, 92857] C189
115) [95621, 1506, 184525] C3 x C189 ---) [61, 753, 95621] C189
116) [102317, 321, 181] C3 x C189 ---) [181, 642, 102317] C189
117) [160373, 1642, 32549] C3 x C189 ---) [269, 821, 160373] C189
118) [179173, 1778, 73629] C3 x C189 ---) [101, 889, 179173] C189
119) [195401, 483, 9472] C3 x C189 ---) [37, 966, 195401] C189
120) [199669, 2402, 643725] C3 x C189 41) [2861, 1201, 199669] C3 x C189
121) [308501, 3010, 1031021] C3 x C189 29) [1949, 1505, 308501] C3 x C189
122) [320377, 619, 15696] C3 x C189 ---) [109, 1238, 320377] C189
123) [365641, 635, 9396] C3 x C189 ---) [29, 1270, 365641] C189
124) [409709, 649, 2873] C3 x C189 ---) [17, 1298, 409709] C189
125) [445433, 675, 2548] C3 x C189 ---) [13, 1350, 445433] C189
126) [482501, 701, 2225] C3 x C189 10) [89, 1402, 482501] C3 x C189
127) [499349, 709, 833] C3 x C189 ---) [17, 1418, 499349] C189
128) [630281, 795, 436] C3 x C189 12) [109, 1590, 630281] C3 x C189
129) [669121, 1175, 177876] C3 x C189 9) [61, 2350, 669121] C3 x C189
130) [733169, 863, 2900] C3 x C189 ---) [29, 1726, 733169] C189
131) [1012397, 1009, 1421] C3 x C189 ---) [29, 2018, 1012397] C189
132) [1072301, 3709, 1026493] C3 x C189 ---) [13, 2073, 1072301] C189
133) [1332769, 3467, 6292] C3 x C189 ---) [13, 2633, 1332769] C189
134) [1474873, 1291, 47952] C3 x C189 ---) [37, 2582, 1474873] C189
135) [1685977, 1435, 93312] C3 x C189 ---) [8, 2870, 1685977] C189
136) [1803337, 4055, 53248] C3 x C189 ---) [13, 2969, 1803337] C189
137) [2001541, 1429, 10125] C3 x C189 ---) [5, 2858, 2001541] C189
138) [2589469, 2217, 581405] C3 x C189 ---) [5, 3241, 2589469] C189
139) [2826181, 2709, 1128125] C3 x C189 ---) [5, 3377, 2826181] C189
140) [2909353, 1721, 13122] C3 x C189 ---) [8, 3442, 2909353] C189
141) [2975209, 2003, 259200] C3 x C189 ---) [8, 4006, 2975209] C189
142) [3001049, 6671, 4373200] C3 x C189 5) [13, 3513, 3001049] C3 x C189
143) [3270461, 2729, 1044245] C3 x C189 ---) [5, 3617, 3270461] C189
144) [3382153, 1859, 18432] C3 x C189 ---) [8, 3718, 3382153] C189
145) [3594169, 1963, 64800] C3 x C189 ---) [8, 3926, 3594169] C189
146) [3894041, 2171, 204800] C3 x C189 ---) [8, 4342, 3894041] C189
147) [4225121, 2511, 520000] C3 x C189 4) [13, 5022, 4225121] C3 x C189
148) [4534729, 2723, 720000] C3 x C189 ---) [8, 5446, 4534729] C189
149) [4740649, 2291, 127008] C3 x C189 ---) [8, 4582, 4740649] C189
150) [5336141, 3281, 1357205] C3 x C189 ---) [5, 4633, 5336141] C189
151) [5780881, 2519, 141120] C3 x C189 2) [5, 5038, 5780881] C3 x C189
152) [7457273, 2731, 272] C3 x C189 ---) [17, 5462, 7457273] C189
153) [8992937, 3059, 91136] C3 x C189 11) [89, 6118, 8992937] C3 x C189
154) [10752617, 4243, 1812608] C3 x C189 ---) [8, 8486, 10752617] C189
155) [14138381, 15009, 52782925] C3 x C189 6) [13, 7929, 14138381] C3 x C189
156) [24065369, 4913, 18050] C3 x C189 3) [8, 9826, 24065369] C3 x C189