manYPoints – Table of Curves with Many Points
Entry details for q =
13
3
= 2197
, g =
5
Table
About
Recent changes
References
Username
Password
Log in
Register
Lower bound
N
min
= 2654
Submitted by
Everett Howe
Date
08-12-2016
Reference
Everett W. Howe
Curves of medium genus with many points
Finite Fields Appl. 47 (2017) 145–160
Comments
Explicit curve: y^2 = x^6 + r^961*x^5 + r^1515*x^4 + r^892*x^3 + r^1700*x^2 + r^684*x + r^1504, z^2 = x^6 + 3*x^5 + r^733*x^4 + r^713*x^3 + r^2014*x^2 + r^1422*x + r^1903, where r^3 + 2*r + 11 = 0.
Tags
Explicit curves
User comments
No comments have been made.
Upper bound
N
max
= 2663
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.