manYPoints – Table of Curves with Many Points
Entry details for q =
23
1
= 23
, g =
5
Table
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Lower bound
N
min
= 66
Earlier entry
Submitted by
Everett Howe
Date
01-08-2022
Reference
Not available
Comments
A search through the genus-5 double covers of genus-2 curves yielded the following example with 66 points:
y^2 = x^6 - 10*x^4 + 4*x^2 - 6
z^2 = y + x^4 + 5*x^2 - 2
Tags
Analysis and enumeration, Explicit curves
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Upper bound
N
max
= 69
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
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