Hello all my colleagues working on automorphism groups of Riemann surfaces;

I have found a method to compute the equation of a Riemann Surface for some given Automorphism Group of certain order.

Then I use the Program "Magma" to check the genus of that surface, but usually it takes a long time.

Is there another program which computes the genus of curve much faster:

For example I am looking for a surface of genus g = 4915.

Can any one of you check the genus of the following curve for me please:

(x1^78 + x2^78 + x3^78) =(x1^26*x2^13 - x1^26*x3^13 - x1^13*x2^26 + x1^13*x3^26 + x2^26*x3^13 - x2^13*x3^26) +(x1^2*x2^2*x3^2)

The Expressions inside the parenthesis are "Primary Invariants" of my Automorphism Group, which must cover a surface of genus g = 4915. So You can even make your own equation using any combination of the primary Invariants and their powers, as long as you come up with a surface of genus g = 4915

Thank all, let me know if you have any question.