Entry details for q = 54 = 625, g = 5
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Lower bound Nmin = 871

Submitted by S.E.Fischer
Date 02/24/2017
Reference Not available
Comments
A corresponding equation is given by
x^4*y^4 + (x^3 + 1)*y^3 + x^2*y^2 + 2*x*y + x^3 = 0.
Tags Explicit curves

User comments

A possibly different curve     
Everett Howe
06/27/2017 20:12
Matthieu Rambaud provides equations for a Shimura curve with 871 points (found in his draft paper "Shimura curves and multiplication"):

3*x^3*y^3 + 2*x^3*y + 4*x^3 + 4*x^2 + 2*x*y^3 + 3*x*y + 3*x + 2 = 0,
3*y^3*z^3 + 2*y^3*z + 4*y^3 + 4*y^2 + 2*y*z^3 + 3*y*z + 3*y + 2 = 0
Upper bound Nmax = 876

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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