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).
Tags Methods from general class field theory

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Explicit Curve     
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. With contributions by Everett Howe, Joseph Oesterlé and Christophe Ritzenthaler. Edited by Alp Bassa, Elisa Lorenzo García, Christophe Ritzenthaler and René Schoof
Documents Mathématiques 18, Société Mathématique de France, Paris, 2020
The Oesterlé bound
Tags Oesterlé bound

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