Dear Researcher in the areas of Topological Groups
I am looking for a MAGMA/GAP program which counts the number of Automorphisms of a Group of automorphisms, without computing all the automorphisms, while the equation of the "Algebraic Curve" and its Genus are known.
Here is the problem:
I am trying to test the number of Automorphisms of an algebraic curve with given equation: X13 + Y13 = X26 Y26 of genus g=235 by MAGMA.
I am hoping that its Automorphism Group is generated by two elements a, b of order 2 & 3 whose product (a*b) has order 78 and the group has order 3042.
I do have a program which computes its Genus pretty fast.
But, when I was trying to find the number of Automorphisms in its Group of Automorphisms using a known program, the program hangs and takes a long time and makes me give up.
Here is what happened for a Galvus Field of p=5737:
F:=GF(5737);
P:=PolynomialRing(F);
R:=PolynomialRing(P);
G := FunctionField(X^13+Y^13 -(X^13*Y^13)^2 );
Genus(G);
235
id := IdentityFieldMorphism(F);
SetVerbose("Aut1", true);
SetVerbose("Aut2", true);
time L := Automorphisms(G : BaseMorphism := id);
Analysing degree one places
Check places of degree 1
After this point, it takes too long and I stopped waiting. Is there a way to test the number of automorphisms in its Group of automorphisms of this curve of genus 235 for me?
Thank you and have a great day! Please write back asap
Dr. Reza Zomorrodian
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