manYPoints – Table of Curves with Many Points
Entry details for q =
13
3
= 2197
, g =
4
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Lower bound
N
min
= 2510
Earlier entry
Later entry
Submitted by
C. Ritzenthaler
Date
02-01-2013
Reference
Not available
Comments
Explicit curve found by M. Afzal Soomro:
y^2=x^3+a^2*x+a^75, z^2=(x+a^323)^3+a^2*(x+a^323)+a^75, where 'a' satisfies t^3+2*t+11=0 over F_13.
Tags
Explicit curves
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Upper bound
N
max
= 2570
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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