manYPoints – Table of Curves with Many Points
Entry details for q =
19
1
= 19
, g =
5
Table
About
Recent changes
References
Username
Password
Log in
Register
Lower bound
N
min
= 55
Earlier entry
Submitted by
Everett Howe
Date
01-07-2022
Reference
Not available
Comments
A search through the genus-5 double covers of genus-2 curves yielded the following example with 55 points:
y^2 = x^5 + 3*x^3 + x^2 + 1
z^2 = y + x^4 + 5*x^3 + 2*x^2 + 8*x + 5
Tags
Analysis and enumeration, Explicit curves
User comments
No comments have been made.
Upper bound
N
max
= 60
Later entry
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.