manYPoints – Table of Curves with Many Points
Entry details for q = 971 = 97, g = 2
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Lower bound Nmin = 136

Submitted by M. Afzal Soomro
Date 04-09-2010
Reference Not available
Comments
Deuring, Max
Die Typen der Multiplikatorenringe elliptischer Funktionenkörper.
Abh. Math. Sem. Hansischen Univ. 14, (1941). 197--272.

This number of point is reached by the curve

y^2=x^6+4*x^4+41*x^2+35.
Tags Formulas for N_q(1) and N_q(2)

User comments

Explicit Curve     
S.E.Fischer
05-19-2016 16:20
We can assume such a curve C as an extension E of degree 3 of a curve F of genus 1 as follows:
F := y^2 + x^3 + 2 ;
E/F := z^3*x + 3*z + 15*x.
Upper bound Nmax = 136

Submitted by Everett Howe
Date 05-03-2010
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
The Hasse-Weil-Serre bound
Tags Hasse-Weil-Serre bound, Formulas for N_q(1) and N_q(2)

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