#12509: computation of height of point on elliptic curve over Q(sqrt(5)) is
WRONG
-----------------------------+----------------------------------------------
Reporter: was | Owner: was
Type: defect | Status: new
Priority: critical | Milestone: sage-5.0
Component: number theory | Keywords:
Work_issues: | Upstream: N/A
Reviewer: | Author:
Merged: | Dependencies:
-----------------------------+----------------------------------------------
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.<a> = 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
}}}
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/12509>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
and MATLAB
--
You received this message because you are subscribed to the Google Groups
"sage-trac" group.
To post to this group, send email to [email protected].
To unsubscribe from this group, send email to
[email protected].
For more options, visit this group at
http://groups.google.com/group/sage-trac?hl=en.
