Entry details for q = 112 = 121, g = 12
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Lower bound Nmin = 338

Submitted by Everett Howe
Date 05-18-2023
Reference Valerio Dose, Guido Lido, Pietro Mercuri, and Claudio Stirpe
Modular curves with many points over finite fields
J. Algebra 635 (2023) 790–821
Comments
Tags Elliptic modular curves

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A (possibly different) curve     
Everett Howe
06-14-2023 02:21
Another example (possibly isomorphic to the submission above) is given by the pair of equations
y^2 := f*(x-r^34)*(x-r^47)*(x-r^76)*(x-r^107)*(x-r^112);
z^2 := f*(x-r^8)*(x-r^13)*(x-r^44)*(x-r^73)*(x-r^86);
where
f := x*(x-1)*(x-r^42)*(x-r^78);
and where r is an element of GF(11^2) with r^2 + 7*r + 2 = 0.
Upper bound Nmax = 386

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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