manYPoints – Table of Curves with Many Points
Entry details for q =
11
2
= 121
, g =
17
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Lower bound
N
min
= 496
Earlier entry
Submitted by
Peter Beelen
Date
09/11/2026
Reference
Peter Beelen, Maria Montanucci, Jonathan Niemann
A maximal function field of genus $17$ over $mathbb{F}_{11^2}$
arXiv
Comments
Curve given by the equations (y^2 −1)^2 = 1−x^12, z^2 = (a+1)f(x)f(ax), where f(x)=(x+1)(x^2+x+1) and a^2=-1.
The automorphism group has order 192.
Details can be found in the following preprint: https://arxiv.org/pdf/2609.11679
Tags
Explicit curves
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Upper bound
N
max
= 496
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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