Entry details for q = 21 = 2, g = 46
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Lower bound Nmin = 36

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 Nmax = 38

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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