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 C945 non-normal (D4) quartic CM field invariants: 146 fields

K Quartic invariants Cl(OK) Igusa invariants Kr Reflex invariants Cl(OKr) Igusa invariants
1) [8, 5470, 7379873] C945 144) [7379873, 2735, 25088] C945
2) [8, 5902, 8577329] C945 ---) [8577329, 2951, 32768] C3 x C945
3) [13, 10161, 25808357] C945 146) [25808357, 17681, 20085637] C945
4) [13, 8622, 18384833] C945 145) [18384833, 4311, 49972] C945
5) [17, 2734, 1433489] C945 129) [1433489, 1367, 108800] C945
6) [17, 2630, 1433017] C945 128) [1433017, 1315, 74052] C945
7) [17, 2830, 1609457] C945 132) [1609457, 1415, 98192] C945
8) [17, 2510, 1573937] C945 131) [1573937, 1255, 272] C945
9) [53, 4390, 4244777] C945 138) [4244777, 2195, 143312] C945
10) [61, 2574, 1640753] C945 133) [1640753, 1287, 3904] C945
11) [89, 1870, 509681] C945 121) [509681, 935, 91136] C945
12) [101, 3806, 2975009] C945 137) [2975009, 1903, 161600] C945
13) [101, 4486, 3576649] C945 ---) [3576649, 2243, 363600] C5 x C945
14) [157, 2598, 1383449] C945 127) [1383449, 1299, 75988] C945
15) [173, 2614, 1572617] C945 130) [1572617, 1307, 33908] C945
16) [241, 4998, 5998217] C945 142) [5998217, 2499, 61696] C945
17) [241, 979, 117604] C945 101) [29401, 1958, 488025] C945
18) [277, 2718, 978209] C945 ---) [978209, 1359, 217168] C3 x C945
19) [277, 1278, 403889] C945 120) [403889, 639, 1108] C945
20) [401, 1067, 81616] C945 ---) [5101, 989, 90225] C189
21) [613, 2006, 652921] C945 123) [652921, 1003, 88272] C945
22) [769, 2511, 1114688] C945 ---) [17417, 2667, 519844] C3 x C945
23) [821, 1353, 383557] C945 119) [383557, 2706, 296381] C945
24) [829, 1425, 497501] C945 ---) [497501, 2850, 40621] C3 x C945
25) [881, 1202, 357677] C945 118) [357677, 601, 881] C945
26) [1093, 2885, 12577] C945 ---) [12577, 2383, 1416528] C3 x C189
27) [1493, 1137, 278029] C945 114) [278029, 2274, 180653] C945
28) [1493, 1113, 246613] C945 112) [246613, 2226, 252317] C945
29) [1601, 202, 3797] C945 ---) [3797, 101, 1601] C135
30) [1601, 251, 12148] C945 ---) [3037, 502, 14409] C135
31) [1601, 587, 37712] C945 ---) [2357, 1174, 193721] C135
32) [1669, 702, 96497] C945 ---) [96497, 351, 6676] C7 x C945
33) [1733, 1053, 255973] C945 ---) [255973, 2106, 84917] C3 x C9 x C945
34) [1733, 830, 144497] C945 108) [144497, 415, 6932] C945
35) [2081, 3106, 6173] C945 ---) [6173, 1553, 601409] C189
36) [2153, 2906, 173509] C945 ---) [3541, 1453, 484425] C189
37) [2153, 834, 165277] C945 ---) [3373, 417, 2153] C189
38) [2393, 2327, 247568] C945 ---) [15473, 4654, 4424657] C5 x C945
39) [2521, 634, 9733] C945 78) [9733, 317, 22689] C945
40) [2609, 1502, 397025] C945 ---) [15881, 751, 41744] C3 x C945
41) [2657, 2287, 669248] C945 ---) [10457, 4574, 2553377] C3 x C945
42) [2969, 3318, 2704777] C945 58) [5113, 1659, 11876] C945
43) [3253, 2997, 449033] C945 ---) [2657, 1663, 637588] C189
44) [3257, 2419, 1279684] C945 73) [6529, 4431, 1302800] C945
45) [3457, 6027, 8935124] C945 98) [18461, 5889, 4234825] C945
46) [3613, 4201, 3038257] C945 81) [10513, 6319, 9769552] C945
47) [3701, 4222, 2975921] C945 ---) [17609, 2111, 370100] C3 x C945
48) [3793, 4603, 3543588] C945 82) [10937, 5667, 8025988] C945
49) [3793, 1435, 400068] C945 85) [11113, 2870, 458953] C945
50) [4093, 2453, 103473] C945 87) [11497, 4906, 5603317] C945
51) [4229, 1337, 65225] C945 ---) [2609, 2674, 1526669] C135
52) [4241, 1295, 333376] C945 60) [5209, 2590, 343521] C945
53) [4273, 2930, 78093] C945 76) [8677, 1465, 517033] C945
54) [4357, 4125, 3677693] C945 ---) [4373, 4281, 4187077] C189
55) [4513, 4646, 5324121] C945 ---) [4889, 2323, 18052] C5 x C945
56) [4513, 4847, 5818068] C945 ---) [17957, 9305, 9969217] C7 x C945
57) [4789, 7493, 1334637] C945 ---) [16477, 7169, 387909] C3 x C945
58) [5113, 1659, 11876] C945 42) [2969, 3318, 2704777] C945
59) [5197, 9413, 12764061] C945 94) [17509, 6917, 2291877] C945
60) [5209, 2590, 343521] C945 52) [4241, 1295, 333376] C945
61) [5273, 295, 9892] C945 ---) [2473, 590, 47457] C135
62) [5393, 8059, 6495764] C945 89) [13421, 6349, 652553] C945
63) [5413, 6605, 9606033] C945 88) [13177, 7175, 12471552] C945
64) [5417, 1399, 455444] C945 ---) [941, 1877, 5417] C135
65) [5417, 986, 48037] C945 ---) [397, 493, 48753] C135
66) [5437, 10121, 13341429] C945 96) [18301, 5753, 8269677] C945
67) [5441, 1498, 16901] C945 ---) [16901, 749, 136025] C7 x C945
68) [5861, 7582, 867937] C945 95) [17713, 3791, 3375936] C945
69) [5869, 5194, 6533125] C945 80) [10453, 2597, 52821] C945
70) [5953, 6871, 5514804] C945 93) [17021, 9261, 20722393] C945
71) [6113, 2155, 46912] C945 ---) [733, 1605, 6113] C3 x C189
72) [6481, 2343, 515300] C945 ---) [5153, 4686, 3428449] C189
73) [6529, 4431, 1302800] C945 44) [3257, 2419, 1279684] C945
74) [7229, 169, 5333] C945 ---) [5333, 338, 7229] C3 x C189
75) [8501, 4721, 2968529] C945 ---) [3089, 3079, 34004] C189
76) [8677, 1465, 517033] C945 53) [4273, 2930, 78093] C945
77) [9029, 2001, 727873] C945 ---) [433, 1163, 325044] C135
78) [9733, 317, 22689] C945 39) [2521, 634, 9733] C945
79) [10357, 1577, 598429] C945 ---) [3541, 3154, 93213] C135
80) [10453, 2597, 52821] C945 69) [5869, 5194, 6533125] C945
81) [10513, 6319, 9769552] C945 46) [3613, 4201, 3038257] C945
82) [10937, 5667, 8025988] C945 48) [3793, 4603, 3543588] C945
83) [10957, 2362, 1000309] C945 ---) [541, 1181, 98613] C135
84) [10957, 2561, 1023349] C945 ---) [3541, 5122, 2465325] C135
85) [11113, 2870, 458953] C945 49) [3793, 1435, 400068] C945
86) [11273, 1702, 2729] C945 ---) [2729, 851, 180368] C189
87) [11497, 4906, 5603317] C945 50) [4093, 2453, 103473] C945
88) [13177, 7175, 12471552] C945 63) [5413, 6605, 9606033] C945
89) [13421, 6349, 652553] C945 62) [5393, 8059, 6495764] C945
90) [13841, 7279, 13242500] C945 ---) [5297, 5227, 885824] C3 x C189
91) [16217, 4115, 3904912] C945 ---) [2017, 5655, 7849028] C135
92) [16901, 2786, 250349] C945 ---) [2069, 1393, 422525] C135
93) [17021, 9261, 20722393] C945 70) [5953, 6871, 5514804] C945
94) [17509, 6917, 2291877] C945 59) [5197, 9413, 12764061] C945
95) [17713, 3791, 3375936] C945 68) [5861, 7582, 867937] C945
96) [18301, 5753, 8269677] C945 66) [5437, 10121, 13341429] C945
97) [18353, 8015, 14734052] C945 ---) [3833, 6991, 8882852] C189
98) [18461, 5889, 4234825] C945 45) [3457, 6027, 8935124] C945
99) [18773, 2246, 59657] C945 ---) [353, 1123, 300368] C189
100) [23629, 2282, 451237] C945 ---) [853, 1141, 212661] C135
101) [29401, 1958, 488025] C945 17) [241, 979, 117604] C945
102) [33029, 645, 95749] C945 ---) [181, 1290, 33029] C189
103) [51137, 247, 2468] C945 ---) [617, 494, 51137] C135
104) [72469, 1202, 71325] C945 ---) [317, 601, 72469] C189
105) [84809, 3070, 999281] C945 ---) [1889, 1535, 339236] C189
106) [85121, 311, 2900] C945 ---) [29, 622, 85121] C135
107) [101021, 393, 13357] C945 ---) [37, 786, 101021] C135
108) [144497, 415, 6932] C945 34) [1733, 830, 144497] C945
109) [170497, 1283, 27904] C945 ---) [109, 2566, 1534473] C189
110) [212081, 1850, 7301] C945 ---) [149, 925, 212081] C189
111) [238141, 2434, 528525] C945 ---) [29, 1217, 238141] C135
112) [246613, 2226, 252317] C945 28) [1493, 1113, 246613] C945
113) [273181, 641, 34425] C945 ---) [17, 1282, 273181] C135
114) [278029, 2274, 180653] C945 27) [1493, 1137, 278029] C945
115) [290369, 541, 578] C945 ---) [8, 1082, 290369] C189
116) [302969, 2410, 240149] C945 ---) [29, 1205, 302969] C189
117) [337121, 589, 2450] C945 ---) [8, 1178, 337121] C135
118) [357677, 601, 881] C945 25) [881, 1202, 357677] C945
119) [383557, 2706, 296381] C945 23) [821, 1353, 383557] C945
120) [403889, 639, 1108] C945 19) [277, 1278, 403889] C945
121) [509681, 935, 91136] C945 11) [89, 1870, 509681] C945
122) [537781, 925, 79461] C945 ---) [109, 1850, 537781] C135
123) [652921, 1003, 88272] C945 21) [613, 2006, 652921] C945
124) [668581, 1269, 235445] C945 ---) [5, 1637, 668581] C135
125) [830153, 2723, 1646144] C945 ---) [89, 5446, 830153] C135
126) [866213, 981, 24037] C945 ---) [13, 1962, 866213] C135
127) [1383449, 1299, 75988] C945 14) [157, 2598, 1383449] C945
128) [1433017, 1315, 74052] C945 6) [17, 2630, 1433017] C945
129) [1433489, 1367, 108800] C945 5) [17, 2734, 1433489] C945
130) [1572617, 1307, 33908] C945 15) [173, 2614, 1572617] C945
131) [1573937, 1255, 272] C945 8) [17, 2510, 1573937] C945
132) [1609457, 1415, 98192] C945 7) [17, 2830, 1609457] C945
133) [1640753, 1287, 3904] C945 10) [61, 2574, 1640753] C945
134) [1695929, 1643, 250880] C945 ---) [5, 2689, 1695929] C135
135) [2026889, 2083, 578000] C945 ---) [5, 2849, 2026889] C189
136) [2178889, 2403, 898880] C945 ---) [5, 2969, 2178889] C189
137) [2975009, 1903, 161600] C945 12) [101, 3806, 2975009] C945
138) [4244777, 2195, 143312] C945 9) [53, 4390, 4244777] C945
139) [4498553, 3595, 2106368] C945 ---) [17, 7190, 4498553] C189
140) [4563737, 2267, 143888] C945 ---) [17, 4534, 4563737] C189
141) [5381881, 2507, 225792] C945 ---) [8, 5014, 5381881] C189
142) [5998217, 2499, 61696] C945 16) [241, 4998, 5998217] C945
143) [6897689, 3067, 627200] C945 ---) [8, 6134, 6897689] C189
144) [7379873, 2735, 25088] C945 1) [8, 5470, 7379873] C945
145) [18384833, 4311, 49972] C945 4) [13, 8622, 18384833] C945
146) [25808357, 17681, 20085637] C945 3) [13, 10161, 25808357] C945