manYPoints – Table of Curves with Many Points
Entry details for q =
17
1
= 17
, g =
9
Table
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Lower bound
N
min
= 72
Earlier entry
Submitted by
Everett Howe
Date
08-12-2025
Reference
Motoko Qiu Kawakita
Fibre products of three hyperelliptic curves with many points
preprint
Comments
Explicit curve: y^2 = (x-1)*(x-12)*(x-16), z^2 = (x-4)*(x-12)*(x-16)*(x-3), w^2 = x*(x-4)*(x-15).
Tags
Fibre products of hyperelliptic curves, Explicit curves
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Upper bound
N
max
= 85
Earlier entry
Later 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 + 8)^7 * (x^2 + 11*x + 29)
Tags
Ihara bound
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