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 10 Igusa CM invariants of cyclic (C4) fields: 17

Number Igusa invariants Conductor Components Quartic invariants Class number Class group
1) [104, 52, 650] [1] 1 [104, 52, 650] 20 C20
2) [104, 52, 26] [1] 1 [104, 52, 26] 20 C20
3) [8, 60, 450] [1] 1 [8, 60, 450] 20 C2 x C10
4) [8, 44, 242] [1] 1 [8, 44, 242] 10 C10
5) [8, 76, 722] [1] 1 [8, 76, 722] 10 C10
6) [5, 345, 23805] [1] 2 [5, 345, 23805] 20 C2 x C10
7) [5, 70, 980] [1] 1 [5, 70, 980] 20 C2 x C10
8) [5, 115, 2645] [1] 2 [5, 115, 2645] 20 C2 x C10
9) [40, 20, 90] [1] 1 [40, 20, 90] 20 C20
10) [113, 339, 16272] [1] 1 [113, 339, 16272] 10 C10
11) [89, 267, 12816] [1] 1 [89, 267, 12816] 10 C10
12) [61, 305, 13725] [1] 1 [61, 305, 13725] 20 C2 x C10
13) [17, 51, 612] [1] 1 [17, 51, 612] 10 C10
14) [17, 51, 612] [2, 2] 2 [17, 51, 612] 10 C10
15) [85, 85, 85] [1] 1 [85, 85, 85] 20 C20
16) [233, 699, 33552] [1] 1 [233, 699, 33552] 10 C10
17) [41, 287, 8036] [1] 1 [41, 287, 8036] 10 C10