manYPoints

Submitted by	Gerrit Oomens
Date	01-01-1900
Reference	Jean-Pierre Serre Sur le nombre de points rationnels d'une courbe algébrique sur un corps fini C. R. Acad. Sci. Paris Sér. I Math. 296 (1983), 397–402. (= Œuvres III, No. 128, 658–663).
Comments
Tags	Methods from general class field theory

Explicit Curve	S.E.Fischer 02-27-2015 15:07
We can assume such a curve C as an extension E of degree 2 of a curve F of genus 2 as follows: F:= y^3 * (x^3 + x) + y^2 * (x^3 + x^2 + x) + 1 ; E/F := z^2 + z + x^3 + x.
Defining equation	Isabel Pirsic 06-18-2012 11:21
E.g., y4([0],[2,1,0],[2,1],[7,3]) = y^4 + (x^2+x+1)y^2 + (x^2+x)y + x^7+ x^3

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
Comments	The Oesterlé bound. Here is a real Weil polynomial that we don't know how to eliminate: x * (x + 2)^2 * (x^2 + 2*x - 2)
Tags	Oesterlé bound

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