Entry details for q = 21 = 2, g = 18
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Lower bound Nmin = 18

Submitted by Gerrit Oomens
Date 01/01/1900
Reference J-P. 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. 664-668).
Comments
Tags Methods from general class field theory

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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 .
Upper bound Nmax = 19

Submitted by Everett Howe
Date 04/14/2010
Reference Jean-Pierre Serre
Rational points on curves over finite fields
Notes by Fernando Q. Gouvêa of lectures at Harvard University, 1985.
Comments
The Oesterlé bound
Tags Oesterlé bound

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