#12356: many missing class number 2 orders in CM j-invariant function over
quadratic fields
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Reporter: cremona | Owner: cremona
Type: defect | Status: needs_review
Priority: major | Milestone: sage-5.0
Component: elliptic curves | Keywords:
Work_issues: | Upstream: N/A
Reviewer: | Author: John Cremona
Merged: | Dependencies:
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Changes (by newvalueoldvalue):
* status: new => needs_review
* author: => John Cremona
Old description:
> In sage/schemes/elliptic_curves/cm.py there is a list of imaginary
> quadratic orders with class number 2, introduced in #11220, but it is
> incomplete! Firstly, discriminant -72 is missing since the paper
> referred to omitted it in error; secondly, all 9 such orders whose
> maximal order has class number 1 were omitted by mistake.
>
> A patch will be provided shortly.
New description:
In sage/schemes/elliptic_curves/cm.py there is a list of imaginary
quadratic orders with class number 2, introduced in #11220, but it is
incomplete! Firstly, discriminant -72 is missing since the paper referred
to omitted it in error; secondly, all 9 such orders whose maximal order
has class number 1 were omitted by mistake.
The patch adds the missing cases and adjusts the doctests (all for
Q(sqrt(5)) whose output is now different as more cases are included.
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Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/12356#comment:1>
Sage <http://www.sagemath.org>
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