manYPoints – Table of Curves with Many Points
Entry details for q =
17
2
= 289
, g =
8
Table
About
Recent changes
References
Username
Password
Log in
Register
Lower bound
N
min
= 562
Submitted by
Carmen Rovi
Date
06-03-2010
Reference
Carmen Rovi
Algebraic Curves over Finite Fields
Comments
Explicit curve: y^17 + 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 22:05
Another equation is given by
y^9 + x^5*y^5 + 9*x^4*y^4 + x^9 = 0.
Upper bound
N
max
= 562
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
User comments
No comments have been made.