Entry details for q = 21 = 2, g = 6
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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).
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Tags Methods from general class field theory

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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
Notes by Fernando Q. Gouvêa of lectures at Harvard University, 1985.
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

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