manYPoints – Table of Curves with Many Points
Entry details for q =
17
4
= 83521
, g =
3
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Lower bound
N
min
= 85256
Submitted by
Everett Howe
Date
05-21-2010
Reference
Not available
Comments
If n is a nonsquare in F_{17^4}, then the hyperelliptic curve n*y^2 = (x + 2)*(x + 10)*(x^2 + 6)*(x^2 + 10)*(x^2 + 6*x + 3) has 85256 points.
Tags
Explicit curves
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Upper bound
N
max
= 85256
Later entry
Submitted by
Everett Howe
Date
05-21-2010
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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