Submitted by 
Gerrit Oomens 
Date 
01/01/1900 
Reference 
JP. Serre Letter to G. van der Geer September 1, 1997.

Comments


Tags 
Methods from general class field theory 
User comments
Correction

S.E.Fischer
12/20/2014 03:42

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^3 + x .

Explicit Curve

S.E.Fischer
12/18/2014 15:30

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 := v^2 + v + x^3 + x .

Defining equation

Isabel Pirsic
06/18/2012 13:00

(x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1)*y^8 +
(x^10 + x^9 + x^6 + x^5 + x + 1)*y^4 +
(x^13 + x^12 + x^11 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2)*y^2 +
(x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^6 + x^5)*y +
x^21 + x^20 + x^17 + x^15 + x^11 + x^10 + x^8 + x^6


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