manYPoints – Table of Curves with Many Points
Entry details for q =
17
1
= 17
, g =
8
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Lower bound
N
min
= 62
Submitted by
thieyacinetop@yahoo.fr
Date
10-14-2016
Reference
Thiéyacine Top
Number of points on a family of curves over a finite field
arXiv:1610.02978 [math.NT]
Comments
y^2=x^5 + 7*x^4 + 8*x^3 + x^2 + 1
z^2=x^5 + 3*x^4 + 16*x^3 + x^2 + 7*x + 4
Tags
Methods from general class field theory
User comments
Explicit Curve
S.E.Fischer
09-10-2019 18:15
Also reached by the curve
y^4 + x^3*y^3 + 13*x^2*y^2 + 15*x*y + x^4 + 3 = 0.
Upper bound
N
max
= 78
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 + 4) * (x + 8)^7
Tags
None
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