#11630: Local data of elliptic curves should not do any global work
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Reporter: wuthrich | Owner: cremona
Type: defect | Status: new
Priority: major | Milestone: sage-4.7.2
Component: elliptic curves | Keywords: Tate's algorithm
Work_issues: | Upstream: N/A
Reviewer: | Author:
Merged: | Dependencies:
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... unless asked to do so.
I am talking about the line 687 in
sage.scheme.elliptic_curves_ell_local_data which reads
{{{
principal_flag = P.is_principal()
if principal_flag:
pi = P.gens_reduced()[0]
verbose("P is principal, generator pi = %s"%pi, t, 1)
else:
pi = K.uniformizer(P, 'positive')
verbose("P is not principal, uniformizer pi = %s"%pi, t, 1)
}}}
While it can be useful, especially when one wants a global minimal model,
it is often very harmful. If the class group of the field is huge or
difficult to compute, one will not be able to determine the fibres of the
Neron model, simply because of this line.
One should add a switch which is by default set to use the second case and
only if needed to the first case.
Of course, in an ideal world Tate's algorithm should be implemented for
any elliptic curve over a local field, rather than a number field.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/11630>
Sage <http://www.sagemath.org>
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