manYPoints – Table of Curves with Many Points
Entry details for q =
7
4
= 2401
, g =
5
Table
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Lower bound
N
min
= 2887
Earlier entry
Submitted by
S.E.Fischer
Date
06/28/2017
Reference
Not available
Comments
An explicit equation is given by
y^5 + r^700*x^3*y^3 + r^50*x^2*y^2 + r^50*x*y + x^5 + r^200 = 0,
where r is a root of the corresponding Primitive Polynomial
X^4 + 5*X^2 + 4*X + 3.
Tags
Explicit curves
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Upper bound
N
max
= 2892
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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