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]

[1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24]
[49][50][51][52][53][54][55][56][57][58][59][60][61][62][63][64][65][66][67][68][69][70][71][72]

Degree 8 Igusa CM invariants of cyclic (C4) fields: 15

Number Igusa invariants Conductor Components Quartic invariants Class number Class group
1) [145, 435, 20880] [1] 1 [145, 435, 20880] 32 C2 x C2 x C8
2) [13, 78, 468] [1] 2 [13, 78, 468] 16 C2 x C2 x C4
3) [8, 84, 882] [1] 2 [8, 84, 882] 16 C2 x C2 x C4
4) [5, 95, 1805] [1] 2 [5, 95, 1805] 16 C2 x C2 x C4
5) [5, 385, 29645] [1] 2 [5, 385, 29645] 16 C2 x C2 x C4
6) [5, 110, 2420] [1] 2 [5, 110, 2420] 16 C2 x C2 x C4
7) [5, 505, 51005] [1] 2 [5, 505, 51005] 16 C4 x C4
8) [5, 465, 43245] [1] 2 [5, 465, 43245] 16 C2 x C2 x C4
9) [40, 60, 90] [1] 1 [40, 60, 90] 16 C2 x C2 x C4
10) [89, 89, 1424] [1] 1 [89, 89, 1424] 8 C2 x C4
11) [37, 111, 2997] [1] 2 [37, 111, 2997] 16 C2 x C2 x C4
12) [17, 85, 1700] [1] 2 [17, 85, 1700] 16 C2 x C2 x C4
13) [17, 102, 2448] [1] 2 [17, 102, 2448] 16 C2 x C2 x C4
14) [65, 455, 12740] [1] 1 [65, 455, 12740] 16 C2 x C2 x C4
15) [65, 65, 260] [1] 1 [65, 65, 260] 16 C2 x C2 x C4