manYPoints – Table of Curves with Many Points
Entry details for q =
7
2
= 49
, g =
12
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Lower bound
N
min
= 190
Earlier entry
Submitted by
Everett Howe
Date
04-14-2026
Reference
Pietro Mercuri, Oana Padurariu, Frederick Saia, and Claudio Stirpe
Point counts, automorphisms, and gonalities of Shimura curves
arXiv:2507.15992 [math.NT]
Comments
Quotient of the Shimura curve X_0^26(57) by the group generated by the Atkin-Lehner involutions w_57 and w_78.
Tags
Shimura curves, Quotients of curves with many points
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Upper bound
N
max
= 214
Submitted by
Everett Howe
Date
04-14-2010
Reference
Everett W. Howe, Kristin E. Lauter
New methods for bounding the number of points on curves over finite fields
Geometry and Arithmetic (C. Faber, G. Farkas, and R. de Jong, eds.), European Mathematical Society, 2012, pp. 173–212
Comments
A real Weil polynomial we don't know how to eliminate: (x + 10) * (x + 14)^11
Tags
None
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