Entry details for q = 27 = 128, g = 5
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Lower bound Nmin = 232

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^19*x + (r^104*x + r^78)/(x^2 + x + 1)
z^2 + z = r^19*x + (r^104*x + r^61)/(x^2 + x + 1) + 1
has genus 5 and has 232 rational points.
Tags Explicit curves, Fibre products of Artin-Schreier curves

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Upper bound Nmax = 234

Submitted by Everett Howe
Date 04/14/2010
Reference E. W. Howe and K. E. Lauter
Improved upper bounds for the number of points on curves over finite fields
Ann. Inst. Fourier (Grenoble) 53 (2003) 1677–1737.
Comments
A real Weil polynomial we don't know how to eliminate: (x^2 + 43*x + 461) * (x^3 + 62*x^2 + 1276*x + 8713)
Tags None

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