Genus 2 Curves Database Igusa CM Invariants Database Quartic CM Fields Database

An Igusa CM invariant is specified by a sequence of three polynomials [ H1(x), G2(x)/N2, G3(x)/N3], such that H1(x), G2(x), and G3(x) are in Z[x],

 H1(i1) = 0, i2 = G2(i1)/N1N2, i3 = G3(i1)/N1N3,
where N1 = H1'(i1), and N2 and N3 are integers, and
 i1 = I4I6/I10, i2 = I23I4/I10, i3 = I22I6/I10,

in terms of the Igusa-Clebsch invariants [ I2, I4, I6, I10 ].

### Degree: [Non-normal] [Cyclic]

 [2] [4] [6] [8] [10] [12] [14] [16] [18] [20] [22] [24] [26] [28] [30] [32] [34] [36] [38] [40] [42] [44] [46] [48] [50] [52] [54] [56] [58] [60] [62] [64] [66] [68] [70] [72] [74] [76] [78] [80] [82] [84] [86] [88] [90] [92] [94] [96] [98] [100] [102] [104] [106] [108] [110] [112] [114] [116] [118] [120] [122] [124] [126] [128] [130] [132] [134] [136] [138] [140] [142] [144] [146] [148] [150] [152] [154] [156] [158] [160] [162] [164] [166] [168] [170] [172] [174] [176] [178] [180] [182] [184] [186] [188] [190] [192] [194] [196] [198] [200] [202] [204] [206] [208] [210] [212] [214] [216] [218] [220] [222] [224] [226] [228] [230] [232] [234] [236] [238] [240] [242] [244] [246] [248] [250] [252] [254] [256] [258] [260] [262] [264] [266] [268] [270] [272] [274] [276] [278] [280] [282] [284] [286] [288] [290] [292] [294] [296] [298] [300] [302] [304] [306] [308] [310] [312] [314] [316] [318] [320] [322] [324] [326] [328] [330] [332] [334] [336] [338] [340] [342] [344] [346] [348] [350] [352] [354] [356] [358] [360] [362] [364] [366] [368] [370] [372] [374] [376] [378] [380] [382] [384] [386] [388] [390] [392] [394] [396] [398] [400] [402] [404] [406] [408] [410] [412] [414] [416] [418] [420] [422] [424] [426] [428] [430] [432] [434] [436] [438] [440] [442] [444] [446] [448] [450] [452] [454] [456] [458] [460] [462] [464] [466] [468] [470] [472] [474] [476] [478] [480] [482] [484] [486] [488] [490] [492] [494] [496] [498] [500] [502] [504] [506] [508] [510] [512] [514] [516] [518] [520] [522] [524] [526] [528] [530] [532] [534] [536] [538] [540] [542] [544] [546] [548] [550] [552] [554] [556] [558] [560] [562] [564] [566] [568] [570] [572] [574] [576] [578] [580] [582] [584] [586] [588] [590] [592] [594] [596] [598] [600] [602] [604] [606] [608] [610] [612] [614] [616] [618] [620] [622] [624] [626] [628] [630] [632] [634] [636] [638] [640] [642] [644] [646] [648] [650] [652] [654] [656] [658] [660] [662] [664] [666] [668] [670] [672] [674] [676] [678] [680] [682] [684] [686] [688] [690] [692] [694] [696] [698] [700] [702] [704] [706] [708] [710] [712] [714] [716] [718] [720] [722] [724] [726] [728] [730] [732] [734] [736] [738] [740] [742] [744] [746] [748] [750] [752] [754] [756] [758] [760] [762] [764] [766] [768] [770] [772] [774] [776] [778] [780] [782] [784] [786] [788] [790] [792] [794] [796] [798] [800] [802] [804] [806] [808] [810] [812] [814] [816] [818] [820] [822] [824] [826] [828] [830] [832] [834] [836] [838] [840] [842] [844] [846] [848] [850] [852] [854] [856] [858] [860] [862] [864] [1106] [1108] [1110] [1112] [1114] [1116] [1118] [1120] [1122] [1124] [1126] [1128] [1130] [1132] [1134] [1136] [1138] [1140] [1142] [1144] [1146] [1148] [1150] [1152]

### Degree 264 Igusa CM invariants of non-normal (D4) fields: 20

 Number Igusa invariants Conductor Components Quartic invariants Class number Class group 1) [269, 353, 27857] [1] 1 [269, 353, 27857] 132 C132 2) [269, 317, 16985] [1] 1 [269, 317, 16985] 132 C2 x C66 3) [269, 293, 10097] [1] 1 [269, 293, 10097] 132 C132 4) [213, 365, 28993] [1] 1 [213, 365, 28993] 132 C132 5) [5, 209, 10769] [11, 11] 1 [5, 209, 10769] 12 C2 x C6 6) [93, 461, 52921] [1] 1 [93, 461, 52921] 132 C2 x C66 7) [413, 281, 14681] [1] 1 [413, 281, 14681] 132 C2 x C66 8) [501, 257, 15385] [1] 1 [501, 257, 15385] 132 C2 x C66 9) [197, 329, 18737] [1] 1 [197, 329, 18737] 132 C132 10) [677, 173, 7313] [1] 1 [677, 173, 7313] 132 C132 11) [677, 305, 21733] [1] 1 [677, 305, 21733] 132 C132 12) [173, 449, 40669] [1] 1 [173, 449, 40669] 132 C132 13) [573, 221, 10921] [1] 1 [573, 221, 10921] 132 C132 14) [77, 361, 28249] [1] 1 [77, 361, 28249] 132 C2 x C66 15) [701, 161, 6305] [1] 1 [701, 161, 6305] 132 C2 x C66 16) [365, 269, 7049] [1] 1 [365, 269, 7049] 264 C2 x C132 17) [101, 457, 51985] [1] 1 [101, 457, 51985] 132 C2 x C66 18) [557, 209, 4097] [1] 1 [557, 209, 4097] 132 C132 19) [557, 329, 15781] [1] 1 [557, 329, 15781] 132 C132 20) [381, 261, 5505] [1] 1 [381, 261, 5505] 132 C2 x C66