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 2 Igusa CM invariants of cyclic (C4) fields: 15

Number Igusa invariants Conductor Components Quartic invariants Class number Class group
1) [13, 221, 3757] [1] 2 [13, 221, 3757] 4 C2 x C2
2) [8, 12, 18] [1] 1 [8, 12, 18] 2 C2
3) [8, 4, 2] [2] 1 [8, 4, 2] 1 C1
4) [5, 15, 45] [1] 2 [5, 15, 45] 4 C2 x C2
5) [5, 105, 2205] [1] 2 [5, 105, 2205] 4 C2 x C2
6) [5, 145, 4205] [1] 2 [5, 145, 4205] 4 C2 x C2
7) [5, 5, 5] [2, 2, 4] 1 [5, 5, 5] 1 C1
8) [5, 30, 180] [1] 2 [5, 30, 180] 4 C2 x C2
9) [5, 5, 5] [2, 2, 2] 1 [5, 5, 5] 1 C1
10) [5, 35, 245] [1] 2 [5, 35, 245] 4 C2 x C2
11) [29, 145, 725] [1] 2 [29, 145, 725] 4 C2 x C2
12) [40, 20, 10] [1] 1 [40, 20, 10] 4 C4
13) [17, 119, 3332] [1] 1 [17, 119, 3332] 2 C2
14) [17, 255, 15300] [1] 2 [17, 255, 15300] 4 C2 x C2
15) [85, 85, 765] [1] 1 [85, 85, 765] 4 C4