manYPoints – Table of Curves with Many Points
Entry details for q =
5
4
= 625
, g =
9
Table
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Lower bound
N
min
= 984
Submitted by
Everett Howe
Date
10-24-2021
Reference
Rohit Gupta, Erik A. R. Mendoza, Luciane Quoos
Reciprocal polynomials and curves with many points over a finite field
Comments
Explicit curve: y^4 = x^4 * (x^4 + u*x^2 + u^7) / (u^7*x^4 + u*x^2 + 1), where u satisfies u^2 + 4*u + 2 = 0.
Tags
Explicit curves
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Upper bound
N
max
= 1076
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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