#5156: [with patch; needs review, doctest fix] implement computation of the
conjectural (analytic) order of Sha for elliptic curves over Heegner
quadratic imaginary fields
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Reporter: was | Owner: was
Type: enhancement | Status: new
Priority: major | Milestone: sage-3.4.1
Component: number theory | Resolution:
Keywords: |
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Comment (by cremona):
PS I meant to say -- beautiful patch! Useful functions, well implemented
and documented.
The function _heegner_index_in_EK() does not really need the Heegned
hypothesis, I think. You do use the fact that K is imaginary quadratic in
the algorithm, but that is all. So you could change checking Heegner hyp.
into checking D<0. It is also tempting to suggest writing a version which
works OK for real quadratic extensions, but I cannot think of a situation
when that would be used (though I guess that Darmon might!)
John
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/5156#comment:12>
Sage <http://sagemath.org/>
Sage - Open Source Mathematical Software: Building the Car Instead of
Reinventing the Wheel
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