manYPoints – Table of Curves with Many Points
Entry details for q =
7
3
= 343
, g =
6
Table
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Lower bound
N
min
= 550
Earlier entry
Submitted by
Everett Howe
Date
08/13/2016
Reference
Everett W. Howe
Curves of medium genus with many points
Finite Fields Appl. 47 (2017) 145–160
Comments
Explicit curve: y^2 = f1*f2, z^2 = f1*f3, where f1 = x^2 + 4, f2 = x^3 + r^56*x^2 + r^68*x + r^194, f3 = x^3 + r^131*x^2 + r^257*x + 1, and where r^3 + 6*r^2 + 4 = 0.
Tags
Explicit curves
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Upper bound
N
max
= 563
Earlier entry
Submitted by
Everett Howe
Date
06/30/2016
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
Obtained using version 1.0 of IsogenyClasses.magma, available at linked URL. A real Weil polynomial we don't know how to eliminate: (x + 34) * (x + 37)^5
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