manYPoints – Table of Curves with Many Points
Entry details for q =
11
4
= 14641
, g =
8
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Lower bound
N
min
= 16546
Later entry
Submitted by
thieyacinetop@yahoo.fr
Date
11-23-2016
Reference
Thiéyacine Top
Number of points on a family of curves over a finite field
arXiv:1610.02978 [math.NT]
Comments
y^2 = x^5 + x^4 + 6*x^2 + 3*x
y^2 = x^5 + x^4 + 6*x^2 + 3*x + 9
Tags
Methods from general class field theory
User comments
Explicit Curve
S.E.Fischer
02-24-2017 21:35
Another equation is given by
(2*x^4 + 1)*y^4 + 9*x^3*y^3 + 9*x*y + 2*x^4 = 0.
Upper bound
N
max
= 16578
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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