The genus 2 package is a Maple package which compute the basic invariants of genus two curves.
Author: T. Shaska
You could also check this page: Genus 2
restart;
with(genus2);
[AutGroup, Clebcsh, CurvDeg3EllSub_J2, Ell_sub_degree_2, FieldOfModuli, Igusa, Info, J_10, J_2, J_4, J_48, J_6, L_2, L_3, L_3_d, LocusCurvesAut_D4, LocusCurvesAut_D4_J2,
LocusCurvesAut_D6, Mestre, ModuliPoint, Obstruction, OrderAutGroup, Rational_model, a_1, a_2, autgroup, i_1, i_2, i_3, sh]
# C:=x^6-x;
# C:=x^5-x;
C:=x^6-1:
# C:=x^6+2*x^4+3*x^2+1;
# C:=x^6+x^3+5;
# C:=x^5+x^3+5*x;
# C:=x^6+3*x^5+x^4+x^3+x^2+x+13;
Info(C,x);
"Initial equation of the curve"
2 6
y = x - 1
"Igusa invariants are [J_2, J_4, J_6, J_10]"
[240, 1620, 119880, 46656]
"Clebcsh invariants are [A, B, C, D]"
[ 2 2 ]
[-2, -, -, 0]
[ 3 9 ]
"The moduli point for this curve is"
[81 -729 729 ]
[--, ----, --------]
[20 200 25600000]
"The Automorphism group is isomorphic to"
[24, 8]
"Sh-invariants are"
[0, 0]
"The minimal field of definition is:"
F=Q
"The field of moduli is:"
M = Q
"The degree of obstraction [F:M] is:"
1
"Rational model is over its minimal field of definition is:"
2 6
y = x - 1
"A minimal rational model is over its minimal field of definition is:"
2 6
y = x - 1
"with moduli point"
[81 -729 729 ]
[--, ----, --------]
[20 200 25600000]