Submitted by 
Gerrit Oomens 
Date 
01/01/1900 
Reference 
JP. Serre Nombre de points des courbes algébriques sur F_q Sém. de Théorie des Nombres de Bordeaux, 1982/83, exp. no. 22. (= Oeuvres III, No. 129, p. 664668).

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Tags 
Methods from general class field theory 
User comments
Explicit Curve

S.E.Fischer
12/18/2014 15:19

We can assume such a curve C as an estension E of degree 2 of an extension F of degree 2 of a maximal curve H of genus 2 as follows:
H:= y^3 * (x^3 + x^2 ) + (x^2+ x +1)*y + 1 ;
F/H := z^2 + z*x^2 + (x^3 + x^2)*y ;
E/(F/H) := v^2 + v*x^2 + x^2 + x .


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