manYPoints – Table of Curves with Many Points
Entry details for q =
2
7
= 128
, g =
6
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Lower bound
N
min
= 251
Earlier entry
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
N
max
= 256
Earlier entry
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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