Entry details for q = 21 = 2, g = 46
Table About Recent changes References
Username
Password
Log in Register

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

User comments

No comments have been made.

Upper bound Nmax = 38

Submitted by Gerrit Oomens
Date 01/01/1900
Reference G. van der Geer, M. van der Vlugt
How to construct curves over finite fields with many points
In: Arithmetic Geometry, (Cortona 1994), F. Catanese Ed., Cambridge Univ. Press, Cambridge, 1997, p. 169-189.
Comments
Tags None

User comments

No comments have been made.