Ok, what I really want to do is determine if there is a torsion point
of order q (a prime) on an elliptic curve over a number field.

Is there a better way to do this in sage besides looking for roots of
the qth division polynomial?

Thanks,
Dan


On May 19, 6:32 pm, "William Stein" <[EMAIL PROTECTED]> wrote:
> On Mon, May 19, 2008 at 6:29 PM, Dan Shumow <[EMAIL PROTECTED]> wrote:
>
> > Presently, in sage, is there anyway to computer the torsion subgroup
> > of a curve over an arbitrary number field?
>
> > I'm pouring through the documentation, and I see how to do it for a
> > curve over the rationals.  Is this not implemented for number fields?
>
> > Thanks,
> > Dan
>
> No, I don't think there is.  I would love for somebody to implement this.
>
> Ifti -- any thoughts -- your thesis was on this sort of thing?
>
> John Cremona -- any thoughts -- this seems right up your ally.
>
> It's funny that we have conductors, tate's algorithm, etc over number
> fields but not torsion.
>
> William
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