manYPoints – Table of Curves with Many Points
Entry details for q =
19
1
= 19
, g =
5
Table
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Lower bound
N
min
= 55
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 55 points:
y^2 = x^5 + 3*x^3 + x^2 + 1
z^2 = y + x^4 + 5*x^3 + 2*x^2 + 8*x + 5
Tags
Analysis and enumeration, Explicit curves
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Upper bound
N
max
= 58
Earlier entry
Later entry
Submitted by
Everett Howe
Date
06-16-2016
Reference
Karl-Otto Stöhr, José Felipe Voloch
Weierstrass points and curves over finite fields
Proc. London Math. Soc. (3) Vol. 52, No. 1 (1986) 1–19
Comments
Proposition 3.1
Tags
Stöhr-Voloch bound
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