manYPoints – Table of Curves with Many Points
Entry details for q =
5
2
= 25
, g =
7
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Lower bound
N
min
= 84
Submitted by
Everett Howe
Date
09/02/2016
Reference
Everett W. Howe
Curves of medium genus with many points
Finite Fields Appl. 47 (2017) 145–160
Comments
Explicit curve: y^2 = r*x^6 + r^21*x^4 + r^9*x^2 + r^13, z^2 = r*x^6 + r^5*x^4 + r^17*x^2 + r^13, where r^2 + 4*r + 2 = 0.
Tags
Explicit curves
User comments
Explicit Curve
S.E.Fischer
02/24/2017 22:30
Another equation is given by
x^4 + y^4 + x^2*y^2+ y^2 + 2*x^2 + 3 = 0,
z^2 + (4*x^2 + 3*y^2) + 2 = 0.
Upper bound
N
max
= 92
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 + 6) * (x + 10)^6
Tags
None
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