manYPoints – Table of Curves with Many Points
Entry details for q =
3
5
= 243
, g =
5
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Lower bound
N
min
= 386
Earlier entry
Submitted by
Everett Howe
Date
08/12/2016
Reference
Everett W. Howe
Curves of medium genus with many points
arXiv:1609.01838 [math.NT]
Comments
Explicit curve: y^2 = x^6 + r^12*x^5 + r^106*x^4 + r^28*x^3 + r^212*x^2 + r^18*x + r^205, z^2 = 2*x^6 + r^202*x^5 + r^39*x^4 + r^76*x^3 + r^169*x^2 + r^180*x + r^167, where r^5 + 2*r + 1 = 0.
Tags
Explicit curves
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Upper bound
N
max
= 397
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 + 29) * (x + 31)^4
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None
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