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 C165 non-normal (D4) quartic CM field invariants: 193 fields

K Quartic invariants Cl(OK) Igusa invariants Kr Reflex invariants Cl(OKr) Igusa invariants
1) [5, 4622, 4854001] C3 x C165 183) [4854001, 2311, 121680] C3 x C165
2) [5, 7198, 11949281] C3 x C165 191) [11949281, 3599, 250880] C3 x C165
3) [5, 10966, 27265769] C3 x C165 193) [27265769, 5483, 699380] C3 x C165
4) [5, 4653, 5320801] C3 x C165 186) [5320801, 3151, 1152000] C3 x C165
5) [5, 6158, 8440561] C3 x C165 ---) [8440561, 3079, 259920] C15 x C825
6) [13, 8150, 15780073] C3 x C165 192) [15780073, 4075, 206388] C3 x C165
7) [13, 3349, 1243141] C3 x C165 163) [1243141, 2453, 1193517] C3 x C165
8) [17, 1078, 229321] C3 x C165 148) [229321, 539, 15300] C3 x C165
9) [17, 1310, 272353] C3 x C165 150) [272353, 655, 39168] C3 x C165
10) [29, 3758, 3411857] C3 x C165 180) [3411857, 1879, 29696] C3 x C165
11) [29, 2774, 1699193] C3 x C165 169) [1699193, 1387, 56144] C3 x C165
12) [61, 3566, 3143953] C3 x C165 ---) [3143953, 1783, 8784] C3 x C15015
13) [101, 958, 189041] C3 x C165 145) [189041, 479, 10100] C3 x C165
14) [113, 5542, 7649513] C3 x C165 189) [7649513, 2771, 7232] C3 x C165
15) [137, 5494, 6485081] C3 x C165 187) [6485081, 2747, 265232] C3 x C165
16) [173, 1574, 342569] C3 x C165 154) [342569, 787, 69200] C3 x C165
17) [229, 1458, 46877] C3 x C165 ---) [46877, 729, 121141] C165
18) [229, 837, 48677] C3 x C165 131) [48677, 1674, 505861] C3 x C165
19) [229, 1590, 12809] C3 x C165 ---) [12809, 795, 154804] C165
20) [257, 3239, 2113856] C3 x C165 ---) [33029, 1709, 721913] C5 x C165
21) [257, 3299, 2666816] C3 x C165 ---) [41669, 2669, 1770473] C165
22) [257, 346, 28901] C3 x C165 ---) [28901, 173, 257] C3 x C495
23) [353, 2918, 2038313] C3 x C165 173) [2038313, 1459, 22592] C3 x C165
24) [569, 3142, 2322377] C3 x C165 177) [2322377, 1571, 36416] C3 x C165
25) [761, 931, 116048] C3 x C165 ---) [7253, 1862, 402569] C165
26) [1069, 1418, 464197] C3 x C165 156) [464197, 709, 9621] C3 x C165
27) [1213, 2518, 13033] C3 x C165 ---) [13033, 1259, 393012] C3 x C2145
28) [1229, 346, 25013] C3 x C165 ---) [25013, 173, 1229] C165
29) [1373, 1621, 406681] C3 x C165 ---) [3361, 1431, 269108] C165
30) [1373, 1818, 161749] C3 x C165 ---) [3301, 909, 166133] C165
31) [1489, 771, 14228] C3 x C165 ---) [3557, 1542, 537529] C165
32) [1597, 546, 68141] C3 x C165 133) [68141, 273, 1597] C3 x C165
33) [1861, 3754, 240325] C3 x C165 90) [9613, 1877, 820701] C3 x C165
34) [2213, 1509, 223489] C3 x C165 ---) [4561, 3018, 1383125] C165
35) [2213, 406, 5801] C3 x C165 ---) [5801, 203, 8852] C165
36) [2213, 169, 2161] C3 x C165 ---) [2161, 338, 19917] C165
37) [2213, 2685, 580177] C3 x C165 ---) [3433, 2399, 717012] C165
38) [2213, 813, 164689] C3 x C165 ---) [3361, 1626, 2213] C165
39) [2237, 6913, 2927249] C3 x C165 115) [17321, 3527, 2585972] C3 x C165
40) [2297, 5723, 56228] C3 x C165 101) [14057, 3095, 1800848] C3 x C165
41) [2557, 2685, 6653] C3 x C165 ---) [6653, 3261, 2457277] C165
42) [2677, 1493, 406681] C3 x C165 ---) [3361, 2986, 602325] C165
43) [2777, 870, 11497] C3 x C165 ---) [11497, 435, 44432] C165
44) [2857, 6046, 9092817] C3 x C165 ---) [12473, 3023, 11428] C165
45) [2857, 2799, 1837892] C3 x C165 ---) [9377, 4791, 559972] C165
46) [2917, 2677, 40653] C3 x C165 ---) [4517, 2557, 1543093] C165
47) [3229, 2021, 32229] C3 x C165 ---) [3581, 3585, 1708141] C165
48) [3229, 3173, 417325] C3 x C165 ---) [16693, 6346, 8398629] C165
49) [3301, 6957, 17477] C3 x C165 ---) [17477, 6337, 1191661] C3 x C3 x C165
50) [3769, 5303, 2544400] C3 x C165 76) [6361, 2795, 1824196] C3 x C165
51) [3877, 1165, 338337] C3 x C165 ---) [4177, 2330, 3877] C165
52) [4001, 290, 5021] C3 x C165 ---) [5021, 145, 4001] C165
53) [4073, 6775, 10732852] C3 x C165 ---) [15877, 5541, 5575937] C3 x C2145
54) [4129, 3803, 716112] C3 x C165 63) [4973, 2721, 1193281] C3 x C165
55) [4201, 2239, 1227024] C3 x C165 83) [8521, 4478, 105025] C3 x C165
56) [4481, 386, 19325] C3 x C165 ---) [773, 193, 4481] C165
57) [4493, 2290, 430397] C3 x C165 ---) [3557, 1145, 220157] C165
58) [4649, 7462, 12730217] C3 x C165 ---) [15137, 3731, 297536] C165
59) [4729, 1947, 606032] C3 x C165 ---) [773, 1093, 4729] C165
60) [4933, 233, 2473] C3 x C165 ---) [2473, 466, 44397] C165
61) [4933, 2893, 19269] C3 x C165 ---) [2141, 1873, 833677] C165
62) [4933, 410, 22293] C3 x C165 ---) [2477, 205, 4933] C165
63) [4973, 2721, 1193281] C3 x C165 54) [4129, 3803, 716112] C3 x C165
64) [5113, 4099, 2972052] C3 x C165 87) [9173, 7585, 14362417] C3 x C165
65) [5261, 4717, 3130625] C3 x C165 ---) [5009, 3211, 2546324] C165
66) [5281, 2006, 668025] C3 x C165 ---) [2969, 1003, 84496] C165
67) [5297, 622, 11969] C3 x C165 ---) [11969, 311, 21188] C165
68) [5309, 845, 17909] C3 x C165 116) [17909, 1690, 642389] C3 x C165
69) [5333, 1466, 3989] C3 x C165 ---) [3989, 733, 133325] C165
70) [5477, 3113, 745361] C3 x C165 ---) [1409, 1643, 547700] C165
71) [5557, 1949, 81369] C3 x C165 86) [9041, 3898, 3473125] C3 x C165
72) [5573, 3333, 1906441] C3 x C165 ---) [5281, 5399, 7222608] C3 x C3 x C165
73) [5653, 4429, 4902597] C3 x C165 92) [11117, 7489, 2990437] C3 x C165
74) [5741, 2602, 1485925] C3 x C165 ---) [1213, 1301, 51669] C165
75) [6133, 3526, 3010041] C3 x C165 ---) [4129, 1763, 24532] C165
76) [6361, 2795, 1824196] C3 x C165 50) [3769, 5303, 2544400] C3 x C165
77) [6637, 1949, 217921] C3 x C165 ---) [1801, 3091, 2150388] C165
78) [6637, 585, 4253] C3 x C165 ---) [4253, 1170, 325213] C165
79) [7753, 2831, 373572] C3 x C165 ---) [1153, 1579, 496192] C165
80) [8017, 371, 16372] C3 x C165 ---) [4093, 742, 72153] C165
81) [8069, 602, 58325] C3 x C165 ---) [2333, 301, 8069] C165
82) [8069, 873, 140101] C3 x C165 ---) [829, 1746, 201725] C165
83) [8521, 4478, 105025] C3 x C165 55) [4201, 2239, 1227024] C3 x C165
84) [8597, 2050, 741133] C3 x C165 ---) [2053, 1025, 77373] C165
85) [8597, 1589, 147649] C3 x C165 ---) [409, 1143, 137552] C165
86) [9041, 3898, 3473125] C3 x C165 71) [5557, 1949, 81369] C3 x C165
87) [9173, 7585, 14362417] C3 x C165 64) [5113, 4099, 2972052] C3 x C165
88) [9281, 1447, 1396] C3 x C165 ---) [349, 1585, 83529] C165
89) [9281, 2798, 620737] C3 x C165 ---) [3673, 1399, 334116] C165
90) [9613, 1877, 820701] C3 x C165 33) [1861, 3754, 240325] C3 x C165
91) [10909, 2666, 685989] C3 x C165 ---) [941, 1333, 272725] C3 x C33
92) [11117, 7489, 2990437] C3 x C165 73) [5653, 4429, 4902597] C3 x C165
93) [12377, 147, 2308] C3 x C165 ---) [577, 294, 12377] C3 x C1155
94) [12401, 1594, 188773] C3 x C165 ---) [1117, 797, 111609] C165
95) [12401, 1267, 26192] C3 x C165 ---) [1637, 2534, 1500521] C165
96) [12401, 615, 91456] C3 x C165 ---) [1429, 1230, 12401] C5 x C165
97) [13537, 1570, 562077] C3 x C165 ---) [173, 785, 13537] C165
98) [13537, 1971, 561716] C3 x C165 ---) [389, 1629, 663313] C165
99) [13537, 1502, 347409] C3 x C165 ---) [4289, 751, 54148] C165
100) [13877, 593, 1181] C3 x C165 ---) [1181, 1186, 346925] C165
101) [14057, 3095, 1800848] C3 x C165 40) [2297, 5723, 56228] C3 x C165
102) [14389, 2297, 711117] C3 x C165 ---) [653, 2693, 1741069] C165
103) [14653, 389, 4861] C3 x C165 ---) [4861, 778, 131877] C165
104) [14969, 3851, 3703808] C3 x C165 ---) [3617, 7702, 14969] C165
105) [15349, 5209, 5398173] C3 x C165 ---) [4957, 8309, 14750389] C165
106) [15641, 5222, 5816297] C3 x C165 ---) [2633, 2611, 250256] C165
107) [15733, 2441, 1454221] C3 x C165 ---) [2749, 4882, 141597] C165
108) [15737, 5158, 2622569] C3 x C165 ---) [2729, 2579, 1007168] C165
109) [15773, 1525, 104273] C3 x C165 ---) [617, 3050, 1908533] C165
110) [16481, 1970, 904301] C3 x C165 ---) [941, 985, 16481] C165
111) [16481, 4119, 3050788] C3 x C165 ---) [4513, 8238, 4763009] C165
112) [16661, 1102, 37025] C3 x C165 ---) [1481, 551, 66644] C165
113) [16661, 1429, 173125] C3 x C165 ---) [277, 1809, 816389] C165
114) [16673, 779, 47504] C3 x C165 ---) [2969, 1558, 416825] C165
115) [17321, 3527, 2585972] C3 x C165 39) [2237, 6913, 2927249] C3 x C165
116) [17909, 1690, 642389] C3 x C165 68) [5309, 845, 17909] C3 x C165
117) [17929, 379, 31428] C3 x C165 ---) [97, 758, 17929] C165
118) [18097, 4207, 3117204] C3 x C165 ---) [1069, 3637, 1465857] C165
119) [18257, 5047, 3515396] C3 x C165 ---) [3041, 6079, 8836388] C165
120) [20693, 882, 111709] C3 x C165 ---) [661, 441, 20693] C165
121) [23297, 1719, 732916] C3 x C165 ---) [109, 1049, 209673] C165
122) [23957, 1965, 671833] C3 x C165 ---) [193, 1311, 383312] C165
123) [24197, 626, 1181] C3 x C165 ---) [1181, 313, 24197] C165
124) [25301, 1501, 253313] C3 x C165 ---) [137, 1279, 404816] C165
125) [25409, 1490, 453389] C3 x C165 ---) [101, 745, 25409] C165
126) [29569, 1583, 27700] C3 x C165 ---) [277, 3166, 2395089] C165
127) [31793, 875, 119872] C3 x C165 ---) [1873, 1750, 286137] C165
128) [35317, 309, 15041] C3 x C165 ---) [89, 618, 35317] C165
129) [35393, 1459, 310964] C3 x C165 ---) [269, 2918, 884825] C165
130) [40093, 898, 41229] C3 x C165 ---) [509, 449, 40093] C165
131) [48677, 1674, 505861] C3 x C165 18) [229, 837, 48677] C3 x C165
132) [57713, 245, 578] C3 x C165 ---) [8, 490, 57713] C3 x C15
133) [68141, 273, 1597] C3 x C165 32) [1597, 546, 68141] C3 x C165
134) [79333, 2254, 801] C3 x C165 ---) [89, 1127, 317332] C165
135) [89417, 2031, 472384] C3 x C165 ---) [61, 2089, 804753] C165
136) [137177, 371, 116] C3 x C165 ---) [29, 742, 137177] C165
137) [143573, 437, 11849] C3 x C165 ---) [41, 874, 143573] C165
138) [146161, 1570, 31581] C3 x C165 ---) [29, 785, 146161] C165
139) [150617, 1615, 313168] C3 x C165 ---) [37, 2421, 150617] C165
140) [151717, 1169, 277] C3 x C165 ---) [277, 2338, 1365453] C165
141) [155501, 401, 1325] C3 x C165 ---) [53, 802, 155501] C165
142) [159569, 421, 4418] C3 x C165 ---) [8, 842, 159569] C165
143) [175061, 485, 15041] C3 x C165 ---) [89, 970, 175061] C165
144) [187417, 3486, 39377] C3 x C165 ---) [233, 1743, 749668] C165
145) [189041, 479, 10100] C3 x C165 13) [101, 958, 189041] C3 x C165
146) [190753, 495, 13568] C3 x C165 ---) [53, 990, 190753] C165
147) [207469, 1529, 532593] C3 x C165 ---) [17, 1823, 829876] C165
148) [229321, 539, 15300] C3 x C165 8) [17, 1078, 229321] C3 x C165
149) [265841, 543, 7252] C3 x C165 ---) [37, 1086, 265841] C165
150) [272353, 655, 39168] C3 x C165 9) [17, 1310, 272353] C3 x C165
151) [273653, 661, 40817] C3 x C165 ---) [17, 1322, 273653] C165
152) [277373, 545, 4913] C3 x C165 ---) [17, 1090, 277373] C165
153) [315617, 1715, 25168] C3 x C165 ---) [13, 1461, 315617] C165
154) [342569, 787, 69200] C3 x C165 16) [173, 1574, 342569] C3 x C165
155) [407489, 639, 208] C3 x C165 ---) [13, 1278, 407489] C165
156) [464197, 709, 9621] C3 x C165 26) [1069, 1418, 464197] C3 x C165
157) [572969, 787, 11600] C3 x C165 ---) [29, 1574, 572969] C165
158) [602489, 2399, 83200] C3 x C165 ---) [13, 2097, 602489] C165
159) [680297, 835, 4232] C3 x C165 ---) [8, 1670, 680297] C3 x C33
160) [1059169, 1487, 288000] C3 x C165 ---) [5, 2061, 1059169] C165
161) [1121017, 1483, 269568] C3 x C165 ---) [13, 2966, 1121017] C165
162) [1162901, 1149, 39325] C3 x C165 ---) [13, 2298, 1162901] C165
163) [1243141, 2453, 1193517] C3 x C165 7) [13, 3349, 1243141] C3 x C165
164) [1252129, 1127, 4500] C3 x C165 ---) [5, 2254, 1252129] C165
165) [1379821, 1329, 96605] C3 x C165 ---) [5, 2597, 1379821] C165
166) [1580633, 1723, 347024] C3 x C165 ---) [41, 3446, 1580633] C165
167) [1610809, 1291, 13968] C3 x C165 ---) [97, 2582, 1610809] C165
168) [1617149, 1273, 845] C3 x C165 ---) [5, 2546, 1617149] C3 x C33
169) [1699193, 1387, 56144] C3 x C165 11) [29, 2774, 1699193] C3 x C165
170) [1744441, 1579, 187200] C3 x C165 ---) [13, 3158, 1744441] C165
171) [1802057, 1891, 443456] C3 x C165 ---) [41, 3782, 1802057] C165
172) [1962209, 1423, 15680] C3 x C165 ---) [5, 2846, 1962209] C165
173) [2038313, 1459, 22592] C3 x C165 23) [353, 2918, 2038313] C3 x C165
174) [2107013, 1461, 6877] C3 x C165 ---) [13, 2922, 2107013] C165
175) [2290889, 2083, 512000] C3 x C165 ---) [5, 3049, 2290889] C165
176) [2318809, 1523, 180] C3 x C165 ---) [5, 3046, 2318809] C165
177) [2322377, 1571, 36416] C3 x C165 24) [569, 3142, 2322377] C3 x C165
178) [2768489, 1939, 247808] C3 x C165 ---) [8, 3878, 2768489] C165
179) [3018217, 1843, 94608] C3 x C165 ---) [73, 3686, 3018217] C165
180) [3411857, 1879, 29696] C3 x C165 10) [29, 3758, 3411857] C3 x C165
181) [4339889, 2087, 3920] C3 x C165 ---) [5, 4174, 4339889] C165
182) [4477961, 2147, 32912] C3 x C165 ---) [17, 4294, 4477961] C165
183) [4854001, 2311, 121680] C3 x C165 1) [5, 4622, 4854001] C3 x C165
184) [4903081, 2227, 14112] C3 x C165 ---) [8, 4454, 4903081] C165
185) [5069849, 2257, 6050] C3 x C165 ---) [8, 4514, 5069849] C165
186) [5320801, 3151, 1152000] C3 x C165 4) [5, 4653, 5320801] C3 x C165
187) [6485081, 2747, 265232] C3 x C165 15) [137, 5494, 6485081] C3 x C165
188) [7319657, 2707, 2048] C3 x C165 ---) [8, 5414, 7319657] C165
189) [7649513, 2771, 7232] C3 x C165 14) [113, 5542, 7649513] C3 x C165
190) [9551033, 3371, 453152] C3 x C165 ---) [8, 6742, 9551033] C165
191) [11949281, 3599, 250880] C3 x C165 2) [5, 7198, 11949281] C3 x C165
192) [15780073, 4075, 206388] C3 x C165 6) [13, 8150, 15780073] C3 x C165
193) [27265769, 5483, 699380] C3 x C165 3) [5, 10966, 27265769] C3 x C165