Here are some functions for genus 2 curves. You can run them on our server here. The input is a genus 2 curve given in Weierstrass equation y^2=a_6 x^6 + ... + a1*x+a0; Enter only C:=a_6*x^6 + ... + a1*x+a0; The moduli point is defined as follows: J_2(C,x); J_4(C,x); J_6(C,x); J_10(C,x) Igusa invariants as defined in [] i_1(C,x), i_2(C,x), i_3(C,x), a_1(C,x(, a_2(C,x), Absolute invariants as defined in []. AutGroup(C,x) Computes the automorphism group of the curve. The autput is given as the GapId for the library of small groups. CurvDeg_3_EllSub(C,x) This function checks if the curve C has a (3, 3)-split Jacobian. CurvDeg3EllSub_J2(C,x) L_3_d(C,x) Ell_sub, J_48, LocusCurvesAut_V4, LocusCurvesAut_D4, LocusCurvesAut_D6, LocusCurvesAut_D4_J2, Rational_model(C,x) Mestre(C,x) An example run in Maple: (There are still some functions which are being implemented). Hopefully will be completed in May 30. > with(genus2); [AutGroup, CurvDeg3EllSub_J2, Ell_sub, 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, OrderAutGroup, Rational_model, a_1, a_2, autgroup, i_1, i_2, i_3, u_v]
>C:=x^6+x^4-x^2+1; 6 4 2 x + x - x + 1 >Info(C,x); "Initial equation of the curve" 6 4 2 "y^2= x + x - x + 1 "Igusa invariants are" [-224, 2128, -140096, -123904] "Clebcsh invariants are" [C2, C4, C6, C10] "The moduli point for this curve is" [171 -23787 29403 ] [---, ------, ---------] [28 2744 275365888] "The Automorphism group is isomorphic to" "The automorphism group is V4": [4,2] "Sh-invariants are" [-1, 0] "The minimal field of definition is:" "F" "The field of moduli is:" "M" "The degree of obstraction is:" "[F:M]=" "Rational model is over its minimal field of definition is:" 6 5 4 3 2 x + 4 x + 60 x - 32 x + 240 x + 64 x + 64 "A minimal rational model is over its minimal field of definition is:" "with moduli point" [171 -23787 29403 ] [---, ------, ---------] [28 2744 275365888] References:
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