manYPoints – Table of Curves with Many Points
Entry details for q =
19
2
= 361
, g =
9
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Lower bound
N
min
= 704
Submitted by
Carmen Rovi
Date
06-03-2010
Reference
Carmen Rovi
Algebraic Curves over Finite Fields
Comments
Explicit curve: y^19 + y = x^2
Found by implementing the method given by Arnaldo Garcia in his paper "Curves over Finite Fields Attaining the Hasse-Weil Upper Bound" Progress in Mathematical Physics, Birkhäuser Verlag, Basel, v. 202, p. 199-205, 2001.
Tags
Explicit curves, Hasse-Weil-Serre bound
User comments
Explicit Curve
S.E.Fischer
02-24-2017 22:11
Another equation is given by
y^6 + x*y + x^6 = 0.
Upper bound
N
max
= 704
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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