I am looking for a MAGMA program which counts the number of Automorphisms of the Group of automorphisms, without necessarily computing all the automorphisms themselves, 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 have found this equation by playing with the “Primary invariants” of a soluble subgroup H of Index [G:H]=9 of a group with presentation:
G:=;
of order 3042
H:=sub;
|H|=338
I NEED A MAGMA Program: Which choses the Equation:
X13 + Y13 = X26 *Y26 Whose genus have been tested to be g=235. show the order of the group covering the above surface is |G|=13(g-1) = 13(235-1) = 3042 Or even order its subgroup |H|= 338. Of course I do know about the following Magma program:
Choose any prime number p
p:=5737;
F:=GF(p);
P:=PolynomialRing(F);
R:=PolynomialRing(P);
G:= FunctionField(X^13+Y^13-X^26*Y^26);
id := IdentityFieldMorphism(F);
SetVerbose("Aut1", true);
SetVerbose("Aut2", true);
time L:=Automorphisms(G : BaseMorphism := id);
Analysing degree one places Check places of degree 1
But this short program takes a very long time and I have not gotten the order with that, because after it gets to:
Analysing degree one places Check places of degree 1, it hangs and made me give up!
Any help with a new MAGMA program will be appreciated.
Regards,
Prof. R. Zomorrodian
Dear Reza, thank you for very interesting information about existing of a program for
a calculation of the automorphism groups for some plane algebraic curves defined over big finite field (and therefore over the field of rational numbers). It is a great surprize for me. Unfortunataly I can not help you with a search of more powerful programs.
Yours respectfully, Marat Gizatullin
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