#5976: [with patch; needs work] Add an Elliptic Curve Isogeny object
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Reporter: shumow | Owner: shumow
Type: enhancement | Status: assigned
Priority: major | Milestone: sage-4.0.1
Component: number theory | Keywords: Elliptic Curves
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Comment(by cremona):
That all sounds very good to me. Yes, over the rationals (and number
fields) one is definitely interested in having specific models of the
codomain. We can add extra bits for the number field case later.
There are of course some striking differences between the number field and
finite field cases. Over finite fields, when two curves are isogenous
there are infinitely many isogenies (e.g.in the ordinary case, the
isogenies form a rank 1 projective module over the endommorphism ring), so
it would not be sufficient just to give the two curves; one might also
want to give a possible degree. While over number fields (amd more
generally in char. 0) there is less choice.
John
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/5976#comment:20>
Sage <http://sagemath.org/>
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