#6455: Bug in twisting for p_primary_bound on Tate-Shafarevich groups
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Reporter: wuthrich | Owner: was
Type: defect | Status: new
Priority: minor | Milestone: sage-4.1.1
Component: number theory | Keywords: Tate Sharafevich group, Elliptic
curves
Reviewer: | Author:
Merged: |
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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.''
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/6455>
Sage <http://sagemath.org/>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
and MATLAB
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