manYPoints – Table of Curves with Many Points
Entry details for q =
71
1
= 71
, g =
4
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Lower bound
N
min
= 132
Later entry
Submitted by
Vijay
Date
04-16-2010
Reference
Vijaykumar Singh, Gary McGuire
The Intersection of Two Fermat Hypersurfaces in P^3 via Computation of Quotient Curves
Comments
The curve of genus 4 defined by the intersection of two Fermat hyper-surfaces x^2+y^2+z^2+w^2=0 and x^3+y^3+z^3+w^3=0 over GF(71) has 132 rational points and hence has defect 4.
Tags
Hasse-Weil-Serre bound
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Upper bound
N
max
= 136
Later entry
Submitted by
Everett Howe
Date
04-14-2010
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
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