#7331: Conditions for non-split multiplicative reduction in p_primary_bound of
Tate-Shafarevich groups
-------------------------------+--------------------------------------------
Reporter: wuthrich | Owner: davidloeffler
Type: defect | Status: needs_work
Priority: minor | Milestone: sage-4.2.1
Component: elliptic curves | Keywords: sha, tate-shafarevich group,
primary bound
Work_issues: | Author: Christian Wuthrich
Reviewer: Robert Miller | Merged:
-------------------------------+--------------------------------------------
Changes (by newvalueoldvalue):
* status: needs_review => needs_work
* reviewer: => Robert Miller
* author: => Christian Wuthrich
Comment:
For `p=3`, an error is getting triggered in computation of the p-adic
regulator:
{{{
sage: E = EllipticCurve('148a')
sage: E.is_surjective(3)
(True, None)
sage: E.has_additive_reduction(3)
False
sage: E.has_nonsplit_multiplicative_reduction(3)
False
sage: E.is_good(3)
True
sage: E.is_ordinary(3)
True
sage: E.sha().p_primary_bound(3)
BOOM
}}}
I have a feeling that this just means that the documentation needs to
include the rank 0 condition when `p=3`:
{{{
E.rank()
1
}}}
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/7331#comment:2>
Sage <http://www.sagemath.org>
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