#13953: (non)archimedian_local_height of a torsion points always gives 0
-------------------------------+--------------------------------------------
Reporter: pbruin | Owner: cremona
Type: defect | Status: new
Priority: major | Milestone: sage-5.7
Component: elliptic curves | Keywords: local heights
Work issues: | Report Upstream: N/A
Reviewers: | Authors:
Merged in: | Dependencies:
Stopgaps: |
-------------------------------+--------------------------------------------
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).
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/13953>
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.
