manYPoints – Table of Curves with Many Points
Entry details for q =
2
1
= 2
, g =
46
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Lower bound
N
min
= 36
Earlier entry
Submitted by
Karl Rökaeus
Date
04/18/2012
Reference
Not available
Comments
Let F be the hyperelliptic genus 2 field given by
y^2 + x*y + x^5 + x^3 + x^2 + x.
Using the notation of Magma, let D be the divisor
(x^3 + x + 1) + (x^2 + x + 1, y + x + 1) +
+(x^2 + x + 1, y + 1)
(The first of the places in the support of D has degree 6, the other two has degree 2.)
Let S be the set of rational places in F.
Then F^D_S, the largest abelian extension of F with conductor <=D such that all places in S split completely, has genus 46 and 36 rational places. This can easily be verified using Magma.
Tags
Methods from general class field theory
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Upper bound
N
max
= 38
Earlier entry
Submitted by
Everett Howe
Date
04/14/2010
Reference
Jean-Pierre Serre
Rational points on curves over finite fields
Notes by Fernando Q. Gouvêa of lectures at Harvard University, 1985.
Comments
The Oesterlé bound
Tags
Oesterlé bound
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