#11220: implement listing j-invariants of CM curves over other fields and fix
incorrect remark in the documentation
-------------------------------+--------------------------------------------
Reporter: was | Owner: cremona
Type: enhancement | Status: needs_review
Priority: minor | Milestone: sage-4.7.1
Component: elliptic curves | Keywords:
Work_issues: | Upstream: N/A
Reviewer: | Author: John Cremona
Merged: | Dependencies:
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Changes (by cremona):
* status: new => needs_review
Old description:
> This email thread says it all:
> {{{
>
> Hi David,
>
> Do you have a list of the CM j-invariants over Q(sqrt(5))?
>
> http://www.sagemath.org/doc/reference/sage/schemes/elliptic_curves/cm.html
>
> -- William
>
> }}}
>
> {{{
> Hi William,
>
> I don't understand the comment (attribution to me) in the doc file.
> I think it is a typo -- replace "field" with "functions" [on modular
> curves of higher level]. In order to solve the problem (as a
> precomputation) over an extension field F, it suffices to factor
> the Hilbert class polynomials. In this case the class number can
> be up to 2 (degree [F:Q]). The attached Magma and Sage code output
> these values for F = Q(sqrt(5)).
>
> Cheers,
>
> David
> }}}
>
> I've attached his files to this ticket.
New description:
This email thread says it all:
{{{
Hi David,
Do you have a list of the CM j-invariants over Q(sqrt(5))?
http://www.sagemath.org/doc/reference/sage/schemes/elliptic_curves/cm.html
-- William
}}}
{{{
Hi William,
I don't understand the comment (attribution to me) in the doc file.
I think it is a typo -- replace "field" with "functions" [on modular
curves of higher level]. In order to solve the problem (as a
precomputation) over an extension field F, it suffices to factor
the Hilbert class polynomials. In this case the class number can
be up to 2 (degree [F:Q]). The attached Magma and Sage code output
these values for F = Q(sqrt(5)).
Cheers,
David
}}}
I've attached his files to this ticket.
Release manager: apply only trac_11220-CM.patch
--
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/11220#comment:3>
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