#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: positive_review
Priority: critical | Milestone: sage-5.0
Component: elliptic curves | Keywords:
Work_issues: | Upstream: N/A
Reviewer: John Cremona, William Stein | Author: John Cremona,
William Stein
Merged: | Dependencies:
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Description changed by 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.
>
> The original patch (by JEC) adds the missing cases and adjusts the
> doctests (all for Q(sqrt(5)) whose output is now different as more cases
> are included. The later patches (by WAS) which are independent, do much
> much more, handling all class numbers up to 100.
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 original patch (by JEC) adds the missing cases and adjusts the
doctests (all for Q(sqrt(5)) whose output is now different as more cases
are included. The later patches (by WAS) which are independent, do much
much more, handling all class numbers up to 100.
Apply trac_12356-cm-rebase-sage5.0.patch and trac_12356-cm-review.patch
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Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/12356#comment:14>
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