Entry details for q = 51 = 5, g = 6
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Lower bound Nmin = 22

Submitted by Oguz Yayla
Date 06/01/2012
Reference Ferruh Özbudak, Burcu Gülmez Temür, Oğuz Yayla
An Exhaustive Computer Search for Finding New Curves with Many Points Among Fibre Products of Two Kummer Covers over GF(5) and GF(7)
Tags Explicit curves

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Explicit equations     
Everett Howe
01/03/2022 00:40
From the cited paper, one finds that the curve defined by the following two equations gives a genus-6 curve over F_5 with 22 points::

y^2 = 3*x^5 + 3*x^4 + 3*x^3 + 3*x^2 + 4
z^2 = 2*x^5 + 3*x^4 + x^3 + 2*x^2 + 2*x + 4
Upper bound Nmax = 24

Submitted by Everett Howe
Date 04/14/2010
Reference Angelika Köhnlein
Obere Schranken für die Punktenzahl von Kurven über endlichen Körpern
Diplomarbeit, Technische Universität Darmstadt, 4 December 2003.
A real Weil polynomial we don't know how to eliminate: (x + 3)^2 * (x^2 + 6*x + 7)^2
Tags None

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