Opened 10 years ago

Closed 10 years ago

#6455 closed defect (fixed)

[with patch, with positive review] Bug in twisting for p_primary_bound on Tate-Shafarevich groups

Reported by: wuthrich Owned by:
Priority: minor Milestone: sage-4.2
Component: elliptic curves Keywords: Tate Sharafevich group, Elliptic curves
Cc: was Merged in: sage-4.2.alpha1
Authors: Chris Wuthrich Reviewers: John Cremona
Report Upstream: Work issues:
Branch: Commit:
Dependencies: Stopgaps:

Description

William Stein found a bug in p_primary_part, namely

sage: E = EllipticCurve([-19,34]); E.cremona_label()  # y^2 = x^3 - 19*x + 34
'944e1'
sage: S = E.sha(); S
Shafarevich-Tate group for the Elliptic Curve defined by y^2 = x^3 -
19*x + 34 over Rational Field
sage: E.ap(5)
-3
sage: factor(944)
2^4 * 59
sage: S.an_padic(5)
Traceback (most recent call last):
...
ValueError: can not twist a curve of conductor (=472) by the quadratic
twist (=-4).

The problem is at 2 and 3, we have to check if we are allowed to twist.

And John Cremona suggested

Is it possible to add a doctest illustrating the suggestion to "try an_padic instead"? That would be useful for the reference manual.

Attachments (1)

trac_6455.patch (3.4 KB) - added by wuthrich 10 years ago.

Download all attachments as: .zip

Change History (9)

comment:1 Changed 10 years ago by davidloeffler

  • Component changed from number theory to elliptic curves
  • Owner changed from was to davidloeffler

comment:2 Changed 10 years ago by wuthrich

  • Cc was added
  • Summary changed from Bug in twisting for p_primary_bound on Tate-Shafarevich groups to [with patch, needs review] Bug in twisting for p_primary_bound on Tate-Shafarevich groups

I believe that the patch chooses now the correct twist.

William : could you use it for the table, before it goes in ? so that I am sure that there are no further problems with it. I have tested it only on a few examples.

Changed 10 years ago by wuthrich

comment:3 Changed 10 years ago by cremona

  • Summary changed from [with patch, needs review] Bug in twisting for p_primary_bound on Tate-Shafarevich groups to [with patch, with positive review] Bug in twisting for p_primary_bound on Tate-Shafarevich groups

Patch applies fine to 4.1.1, and tests run ok. The code looks ok to me too. I'm not quite expert enough to be 100% confident, but enough to pass this!

comment:4 Changed 10 years ago by cremona

  • Authors set to Chris Wuthrich
  • Reviewers set to John Cremona

comment:5 Changed 10 years ago by jason

  • Status changed from new to needs_review

comment:6 Changed 10 years ago by jason

  • Status changed from needs_review to positive_review

comment:7 Changed 10 years ago by davidloeffler

  • Owner changed from davidloeffler to (none)

comment:8 Changed 10 years ago by mhansen

  • Merged in set to sage-4.2.alpha1
  • Resolution set to fixed
  • Status changed from positive_review to closed
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