manYPoints – Table of Curves with Many Points
Entry details for q =
3
4
= 81
, g =
7
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Lower bound
N
min
= 196
Earlier entry
Submitted by
Everett Howe
Date
09-02-2016
Reference
Everett W. Howe
Curves of medium genus with many points
Finite Fields Appl. 47 (2017) 145–160
Comments
Explicit curve: y^2 = x^6 + r^70*x^2 + r^50, z^2 = x^6 + r^50*x^2 + r^70, where r^4 + 2*r^3 + 2 = 0.
Tags
Explicit curves
User comments
Explicit Curve
S.E.Fischer
03-20-2017 16:20
Another equation is given by
2*y^6 + x^5*y^5 + 2*x^4*y^4 + 2*x^3*y^3 + 2*x^2*y^2 + x*y + x^6 = 0.
Upper bound
N
max
= 208
Earlier 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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