manYPoints – Table of Curves with Many Points
Entry details for q = 22 = 4, g = 44
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Lower bound Nmin = 71

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_0^1589(1) by the Atkin-Lehner involution w_1589.
Tags Shimura curves, Quotients of curves with many points

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Upper bound Nmax = 83

Submitted by Gerrit Oomens
Date 01-01-1900
Reference Gerard van der Geer, Marcel van der Vlugt
How to construct curves over finite fields with many points
In: Arithmetic Geometry, (Cortona 1994), F. Catanese Ed., Cambridge Univ. Press, Cambridge, 1997, p. 169-189.
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