Entry details for q = 53 = 125, g = 6
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Lower bound Nmin = 244

Submitted by Everett Howe
Date 08/13/2016
Reference Everett W. Howe
Curves of medium genus with many points
arXiv:1609.01838 [math.NT]
Comments
Explicit curve: y^2 = f1*f2, z^2 = f1*f3, where f1 = x^2 + 4*x, f2 = x^3 + r^21*x^2 + r^102*x + r^3, f3 = x^3 + r^91*x^2 + r^63*x + r^21, and where r^3 + 3*r + 3 = 0.
Tags Explicit curves

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Upper bound Nmax = 255

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 + 19) * (x + 22)^5
Tags None

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