Submitted by 
Gerrit Oomens 
Date 
01011900 
Reference 
JeanPierre Serre Letter to G. van der Geer September 1, 1997.

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Tags 
Methods from general class field theory 
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Correction

S.E.Fischer
12202014 03:39

The extension E/F leads to a curve of genus 4 with 8 points. Extending once again by H of degree 2 leads to the desired result, as we write
H/(E/F):= v^2 + v*x + x^3 + x .

Explicit Curve

S.E.Fischer
12182014 15:27

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

My reference corrected

Isabel Pirsic
06192012 16:18

G. van der Geer
Hunting for curves over finite fields with many points
arXiv:0902.3882

Defining equation

Isabel Pirsic
06192012 14:17

y^8 +
(x^4 + x + 1)*y^4 +
(x^2 + x)*y^2 +
(x^4 + x^2)*y +
(x^12 + x^4)
Ref: 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.


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