Entry details for q = 21 = 2, g = 6
Table About Recent changes References
Username
Password
Log in Register

Lower bound Nmin = 10

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

User comments

Explicit Curve     
S.E.Fischer
12/18/2014 15:42
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^2 ) + (x^2+ x +1)*y + 1 ;
E/F := z^2 + z*x^2 + (x^3 + x^2)*y .
Upper bound Nmax = 10

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 - 1) * (x + 2) * (x^2 + 3*x + 1)^2
Tags Oesterlé bound

User comments

No comments have been made.