Entry details for q = 27 = 128, g = 6
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Lower bound Nmin = 251

Submitted by Everett Howe
Date 05/20/2020
Reference Not available
Comments
Let r be an element of F_128 that satisfies r^7 + r + 1 = 0. Then the curve C over F_128 defined by the two equations
y^2 + y = r^23*x + r^75/(x^2 + x) + 1
z^2 + z = r^75*x + r^101/(x^2 + x) + 1
has genus 6 and has 251 rational points.
Tags Explicit curves, Fibre products of Artin-Schreier curves

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Upper bound Nmax = 256

Submitted by Everett Howe
Date 04/14/2010
Reference Everett W. Howe and 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^2 + 41*x + 417) * (x^2 + 43*x + 461)^2
Tags None

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