manYPoints – Table of Curves with Many Points
Entry details for q =
5
4
= 625
, g =
3
Table
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Lower bound
N
min
= 776
Submitted by
Everett Howe
Date
05-20-2010
Reference
Not available
Comments
If r is an element of F_{5^4} with r^4 - r^2 - r + 2 = 0, then the hyperelliptic curve
y^2 = r*x^8 + r^464*x^6 + r^298*x^2 + r^449
has 776 points.
Tags
Explicit curves
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Upper bound
N
max
= 776
Later entry
Submitted by
Everett Howe
Date
05-20-2010
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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