manYPoints – Table of Curves with Many Points
Entry details for q = 53 = 125, g = 4
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Lower bound Nmin = 210

Submitted by Everett Howe
Date 02-16-2014
Reference Everett W. Howe
Quickly constructing curves of genus 4 with many points
Frobenius Distributions: Sato–Tate and Lang–Trotter conjectures (D. Kohel and I. Shparlinski, eds.), Contemporary Mathematics 663, American Mathematical Society, Providence, RI, 2016, pp. 149–173
Comments
Explicit curve: y^2 = x^3 + a^35*x + a^7, z^2 = x^3 + 2*x^2 + a^85*x + a^107, where a^3 + 3*a + 3 = 0.
Tags Explicit curves

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Upper bound Nmax = 211

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 + 19) * (x + 22)^3
Tags None

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