Submitted by 
Gerrit Oomens 
Date 
01/01/1900 
Reference 
G. van der Geer, M. van der Vlugt How to construct curves over finite fields with many points In: Arithmetic Geometry, (Cortona 1994), F. Catanese Ed., Cambridge Univ. Press, Cambridge, 1997, p. 169189.

Comments


Tags 
Fibre products of ArtinSchreier curves 
User comments
Explicit Curve

S.E.Fischer
12/07/2014 04:13

We can assume such a curve C as an extension C' of degree 2 of a maximal curve M of genus 1 as follows:
M := (x + y + x*y) * (x*y) +1 ;
C'/M := z^2 + z*(x*y^5)+ x^2*y^5 .

Explicit Curve

S.E.Fischer
12/07/2014 04:10

We can assume such a curve C as an extension C' of degree 2 of a maximal curve of genus 1 as follows:
C' := (x + y + x*y) * (x*y) +1 ;
C/C' := z^2 + z*(x*y^5)+ x^2*y^5 .


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