Entry details for q = 191 = 19, g = 5
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Lower bound Nmin = 54

Submitted by Everett Howe
Date 08-12-2016
Reference Everett W. Howe
Curves of medium genus with many points
Finite Fields Appl. 47 (2017) 145–160
Comments
Explicit curve: y^2 = x^6 + 6*x^5 + 9*x^4 + 11*x^3 + 4*x^2 + 4*x + 8, z^2 = x^6 + 17*x^5 + 12*x^4 + 13*x^3 + 18*x^2 + x + 4.
Tags Explicit curves

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Upper bound Nmax = 57

Submitted by Everett Howe
Date 06-16-2016
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
Obtained using version 1.0 of IsogenyClasses.magma, available at linked URL. A real Weil polynomial we don't know how to eliminate: (x + 5) * (x + 8)^4
Tags None

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