manYPoints – Table of Curves with Many Points
Entry details for q =
19
5
= 2476099
, g =
7
Table
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Lower bound
N
min
= 2498052
Earlier entry
Submitted by
Everett Howe
Date
04-04-2017
Reference
Everett W. Howe
Curves of medium genus with many points
Finite Fields Appl. 47 (2017) 145–160
Comments
Explicit curve:
y^2 = 2*x^3 + r^1369457*x^2 + r^537343*x
z^2 = 2*x^3 + r^944216*x^2 + r^1918843*x + r^790050
w^2 = 2*x^3 + r^1174303*x^2 + r^534223*x
where r^5 + 5*r + 17 = 0.
Tags
Explicit curves
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Upper bound
N
max
= 2498129
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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