manYPoints – Table of Curves with Many Points
Entry details for q =
2
2
= 4
, g =
11
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Lower bound
N
min
= 28
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_0^4485(1) by the group generated by the Atkin-Lehner involutions w_3, w_13, and w_115.
Tags
Quotients of curves with many points, Shimura curves
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Upper bound
N
max
= 29
Earlier entry
Submitted by
Everett Howe
Date
04-14-2010
Reference
E. W. Howe, K. E. Lauter
Improved upper bounds for the number of points on curves over finite fields
Ann. Inst. Fourier (Grenoble) 53 (2003) 1677–1737.
Comments
A real Weil polynomial we don't know how to eliminate: (x - 1) * (x + 1)^2 * (x + 2)^4 * (x + 3) * (x + 4)^3
Tags
None
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