manYPoints – Table of Curves with Many Points
Entry details for q =
7
4
= 2401
, g =
7
Table
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Lower bound
N
min
= 3072
Earlier entry
Submitted by
Everett Howe
Date
09-02-2016
Reference
Everett W. Howe
Curves of medium genus with many points
Finite Fields Appl. 47 (2017) 145–160
Comments
Explicit curve: y^2 = r*x^6 + 6*x^4 + r^1999*x^2 + r^798, z^2 = x^6 + r^1199*x^4 + r^398*x^2 + r^1597, where r^4 + 5*r^2 + 4*r + 3 = 0.
Tags
Explicit curves
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Upper bound
N
max
= 3088
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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