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Explicit Curve

S.E.Fischer
11/27/2014 23:10

We can construct such a curve C as an deg2 extension of a curve C' of genus 2 as follows:
C': y^3 *( x^3 + x ) + y * (x^3 + x^2 + x) + 1
C/C': z^2 + z + x^3 + x
This information, appropriately provided for MAGMA, reads as:
> R<x> := FunctionField(GF(2));
> P<y> := PolynomialRing(R);
> S<z> := PolynomialRing(P);
FF := FunctionField( y^3 *( x^3 + x ) + y * (x^3 + x^2 + x) + 1 );
> FF;
F := ( ext < FF  z^2 + z + x^3 + x >);
F;
print "Genus =", Genus(F);
print "NoP =", #Places(F,1);
print Places(F,1);


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