There was  another similar thread a few days ago, with a little more
information.  It would actually not be difficult to get this working
naturally (famous last words).

There is quite an old ticket already out for this (#1975, see
http://trac.sagemath.org/sage_trac/ticket/1975).

John

On May 3, 9:34 am, Jeroen Demeyer <jdeme...@cage.ugent.be> wrote:
> Hello sage-support,
>
> I wonder if there is a way to make Sage compute with points on elliptic
> curves over rings which are not fields.  I would like to use it for a
> very simple implementation of the ECM factoring algorithm for
> educational purposes.  The obvious doesn't work:
>
> ----------------------------------------------------------------------
> | Sage Version 4.4, Release Date: 2010-04-24                         |
> | Type notebook() for the GUI, and license() for information.        |
> ----------------------------------------------------------------------
> sage: R = Zmod(59*101)
> sage: E = EllipticCurve(R, [4,1])
> sage: P = E([0,1])
> ---------------------------------------------------------------------------
> NotImplementedError
> [...]
>
> Thanks,
> Jeroen Demeyer.
>
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