On Tue, May 20, 2008 at 6:02 PM, Dan Shumow <[EMAIL PROTECTED]> wrote: > > 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? >
It depends on the elliptic curve and on q. A standard technique for dealing with the sort of problem, in particular, for ruling out the existence of such a point is to use that the reduction map from E(K)[q] --> E(F_r)[q] is injective under appropriate hypothesis. Then you compute #E(F_r) quickly and if this is coprime to q then you definitely have no q-torsion over E(K). -- William --~--~---------~--~----~------------~-------~--~----~ To post to this group, send email to [email protected] To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/sage-support URLs: http://www.sagemath.org -~----------~----~----~----~------~----~------~--~---
