#10096: sha().an() assumes E is minimal.
-------------------------------+--------------------------------------------
Reporter: weigandt | Owner: cremona
Type: defect | Status: new
Priority: major | Milestone: sage-4.6
Component: elliptic curves | Keywords: elliptic curves, sha, real
period
Author: | Upstream: Reported upstream. Developers
acknowledge bug.
Reviewer: | Merged:
Work_issues: |
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I noticed the following problem with sha().an()
{{{
sage: E=EllipticCurve([1215*1216,0]) # non-minimal model
sage: E.sha().an()
6.00000000000000
sage: E.minimal_model().sha().an()
1.00000000000000
}}}
It looks like sha().an() assumes that E is minimal. The extra factor of 6
seems to be coming from the real period.
{{{
sage: E.period_lattice().omega()
0.106360349280819
sage: E.minimal_model().period_lattice().omega()
0.638162095684913
}}}
It's probably unfair to call this a bug, but it could definitely lead
people astray.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/10096>
Sage <http://www.sagemath.org>
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