id,summary,reporter,owner,description,type,status,priority,milestone,component,resolution,keywords,cc,merged,author,reviewer,upstream,work_issues,branch,commit,dependencies,stopgaps
12509,computation of height of point on elliptic curve over Q(sqrt(5)) is WRONG,was,was,"There are evidently many examples in which computing {{{P.height()}}}, for {{{P}}} a point on an elliptic curve over Q(sqrt(5)) yields a completely wrong answer. This is very serious, since it is a blatantly wrong mathematical answer -- raising NotImplementedError would be much better! Here's an example that Ashwath Rabindranath (Princeton) found, where Sage and Magma do not agree. According to BSD, Sha has order 1 using the Magma answer, and a crazy order with the Sage answer.
{{{
sage: K. = NumberField(x^2-x-1)
sage: v = [0, a + 1, 1, 28665*a - 46382, 2797026*a - 4525688]
sage: E = EllipticCurve(v)
sage: E == E.global_minimal_model()
True
sage: F.a_invariants()
(0, a + 1, 1, 28665*a - 46382, 2797026*a - 4525688)
sage: P = E([72*a - 509/5, -682/25*a - 434/25])
sage: P.height()
1.35648516097058
sage: Q = magma(E)(magma([P[0], P[1]]))
sage: Q
(1/5*(360*a - 509) : 1/25*(-682*a - 434) : 1)
sage: Q.Height()
1.38877711688727252538242306
}}}
Apply: [attachment:trac12509-heights.patch], [attachment:trac12509-heights2.patch], [attachment:trac12509-heights3.patch]",defect,closed,critical,sage-5.10,elliptic curves,fixed,heights,,sage-5.10.beta3,John Cremona,"Peter Bruin, Chris Wuthrich",N/A,,,,,#12692