manYPoints – Table of Curves with Many Points
Entry details for q =
17
1
= 17
, g =
5
Table
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Lower bound
N
min
= 51
Earlier entry
Submitted by
Everett Howe
Date
01-07-2022
Reference
Not available
Comments
A search through the genus-5 double covers of genus-2 curves yielded the following example with 51 points:
y^2 = x^5 - 5*x^4 + x^3 + 4*x^2 + 8*x - 8
z^2 = x*y + x^4 - 7*x^3 + 6*x^2 - 8*x - 4
Tags
Analysis and enumeration, Explicit curves
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Upper bound
N
max
= 53
Submitted by
Everett Howe
Date
04-14-2010
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
A real Weil polynomial we don't know how to eliminate: (x + 7)^5
Tags
None
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