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 4 Igusa CM invariants of cyclic (C4) fields: 19

Number Igusa invariants Conductor Components Quartic invariants Class number Class group
1) [109, 545, 68125] [1] 2 [109, 545, 68125] 8 C2 x C4
2) [205, 205, 1845] [1] 1 [205, 205, 1845] 8 C2 x C4
3) [136, 68, 850] [1] 1 [136, 68, 850] 8 C2 x C4
4) [13, 273, 5733] [1] 2 [13, 273, 5733] 8 C2 x C2 x C2
5) [13, 13, 13] [3, 3] 1 [13, 13, 13] 1 C1
6) [13, 39, 117] [1] 2 [13, 39, 117] 8 C2 x C2 x C2
7) [8, 68, 578] [1] 2 [8, 68, 578] 8 C2 x C4
8) [8, 28, 98] [1] 1 [8, 28, 98] 4 C2 x C2
9) [5, 55, 605] [1] 2 [5, 55, 605] 8 C2 x C2 x C2
10) [5, 305, 18605] [1] 2 [5, 305, 18605] 8 C2 x C4
11) [5, 165, 5445] [1] 2 [5, 165, 5445] 8 C2 x C2 x C2
12) [5, 205, 8405] [1] 2 [5, 205, 8405] 8 C2 x C4
13) [5, 285, 16245] [1] 2 [5, 285, 16245] 8 C2 x C2 x C2
14) [221, 221, 10829] [1] 1 [221, 221, 10829] 8 C2 x C4
15) [17, 17, 68] [1] 1 [17, 17, 68] 4 C2 x C2
16) [17, 34, 272] [1] 1 [17, 34, 272] 4 C2 x C2
17) [73, 219, 10512] [1] 1 [73, 219, 10512] 4 C2 x C2
18) [41, 41, 164] [1] 1 [41, 41, 164] 4 C2 x C2
19) [65, 195, 9360] [1] 1 [65, 195, 9360] 8 C2 x C4