id,summary,reporter,owner,description,type,status,priority,milestone,component,resolution,keywords,cc,merged,author,reviewer,upstream,work_issues,branch,commit,dependencies,stopgaps
6455,"[with patch, with positive review] Bug in twisting for p_primary_bound on Tate-Shafarevich groups",wuthrich,,"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.''
",defect,closed,minor,sage-4.2,elliptic curves,fixed,"Tate Sharafevich group, Elliptic curves",was,sage-4.2.alpha1,Chris Wuthrich,John Cremona,,,,,,