manYPoints – Table of Curves with Many Points
Entry details for q =
5
2
= 25
, g =
22
Table
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Lower bound
N
min
= 174
Earlier entry
Submitted by
Everett Howe
Date
10-24-2021
Reference
Rohit Gupta, Erik A. R. Mendoza, Luciane Quoos
Reciprocal polynomials and curves with many points over a finite field
Comments
Explicit curve given by the two equations y^3 = (x^2 + 1)^2 / x^2 and z^6 = (x^2 + 4) * (4*x^2 + 1) / x^5.
Tags
Explicit curves
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Upper bound
N
max
= 208
Earlier entry
Submitted by
Everett Howe
Date
04-14-2010
Reference
Yasutaka Ihara
Some remarks on the number of rational points of algebraic curves
J. Fac. Sci. Univ. Tokyo Sect. IA Math. 28 (1981) 721–724 (1982)
Comments
The Ihara bound. Here is a real Weil polynomial that we don't know how to eliminate: (x + 6) * (x + 8)^14 * (x + 9)^6 * (x + 10)
Tags
Ihara bound
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