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 5 Igusa CM invariants of cyclic (C4) fields: 14

Number Igusa invariants Conductor Components Quartic invariants Class number Class group
1) [157, 157, 1413] [1] 1 [157, 157, 1413] 5 C5
2) [349, 349, 28269] [1] 1 [349, 349, 28269] 5 C5
3) [8, 52, 338] [1] 2 [8, 52, 338] 10 C10
4) [5, 185, 6845] [1] 2 [5, 185, 6845] 10 C10
5) [5, 265, 14045] [1] 2 [5, 265, 14045] 10 C10
6) [5, 365, 26645] [1] 2 [5, 365, 26645] 10 C10
7) [5, 130, 3380] [1] 4 [5, 130, 3380] 20 C2 x C10
8) [53, 265, 1325] [1] 2 [53, 265, 1325] 10 C10
9) [37, 481, 56277] [1] 2 [37, 481, 56277] 10 C10
10) [37, 185, 8325] [1] 2 [37, 185, 8325] 10 C10
11) [197, 197, 9653] [1] 1 [197, 197, 9653] 5 C5
12) [373, 373, 30213] [1] 1 [373, 373, 30213] 5 C5
13) [173, 173, 173] [1] 1 [173, 173, 173] 5 C5
14) [101, 101, 2525] [1] 1 [101, 101, 2525] 5 C5