#13953: (non)archimedian_local_height of a torsion points always gives 0
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Reporter: pbruin | Owner: cremona
Type: defect | Status: needs_review
Priority: major | Milestone: sage-5.7
Component: elliptic curves | Resolution:
Keywords: local heights | Work issues:
Report Upstream: N/A | Reviewers:
Authors: Peter Bruin | Merged in:
Dependencies: | Stopgaps:
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Changes (by {'newvalue': u'Peter Bruin', 'oldvalue': ''}):
* status: new => needs_review
* author: => Peter Bruin
Old description:
> For torsion points of elliptic curves over number fields,
> nonarchimedian_local_height incorrectly returns 0, and
> archimedian_local_height raises an error:
> {{{
> sage: K.<i> = QuadraticField(-1)
> sage: E = EllipticCurve([0, 0, 0, K(1), 0])
> sage: P = E(i, 0)
> sage: P.nonarchimedian_local_height()
> 0
> sage: P.archimedian_local_height()
> NameError: global name 'QQ' is not defined
> }}}
>
> The correct behaviour (for the normalisation used in Sage) is
> {{{
> sage: P.nonarchimedian_local_height()
> -1/2*log(2)
> sage: P.archimedian_local_height()
> 0.346573590279973
> }}}
>
> Note: the same would happen for rational points on elliptic curves over
> Q, but computing local heights over Q is broken (see #13951).
New description:
For torsion points of elliptic curves over number fields,
nonarchimedian_local_height incorrectly returns 0, and
archimedian_local_height raises an error:
{{{
sage: K.<i> = QuadraticField(-1)
sage: E = EllipticCurve([0, 0, 0, K(1), 0])
sage: P = E(i, 0)
sage: P.nonarchimedian_local_height()
0
sage: P.archimedian_local_height()
NameError: global name 'QQ' is not defined
}}}
The correct behaviour (for the normalisation used in Sage) is
{{{
sage: P.nonarchimedian_local_height()
-1/2*log(2)
sage: P.archimedian_local_height()
0.346573590279973
}}}
Note: the same would happen for rational points on elliptic curves over Q,
but computing local heights over Q is broken (see #13951).
Apply: trac13953-local_heights_torsion.patch
--
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Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/13953#comment:1>
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