[with patch, with positive review] Bug in twisting for p_primary_bound on Tate-Shafarevich groups
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.
Change History (9)
Component: |
number theory →
elliptic curves
|
Owner: |
changed from William Stein to David Loeffler
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Cc: |
William Stein added
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Summary: |
Bug in twisting for p_primary_bound on Tate-Shafarevich groups →
[with patch, needs review] Bug in twisting for p_primary_bound on Tate-Shafarevich groups
|
Summary: |
[with patch, needs review] Bug in twisting for p_primary_bound on Tate-Shafarevich groups →
[with patch, with positive review] Bug in twisting for p_primary_bound on Tate-Shafarevich groups
|
Authors: |
→ Chris Wuthrich
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Reviewers: |
→ John Cremona
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Status: |
new →
needs_review
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Status: |
needs_review →
positive_review
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Owner: |
David Loeffler deleted
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Merged in: |
→ sage-4.2.alpha1
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Resolution: |
→ fixed
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Status: |
positive_review →
closed
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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.