On 8/6/07, Joseph Hufnagle <[EMAIL PROTECTED]> wrote: > > Mr. Stein, > Given an elliptic curve defined as > > > e=EllipticCurve([-1386747,368636886]);e > > how does one find the torsion points? e.torsion_order() and > e.torsion_subgroup() give information about the order, but no points.
Great question. Here's an example (which I've also added to the SAGE documentation so in future people are less likely to be confused): sage: e=EllipticCurve([-1386747,368636886]);e Elliptic Curve defined by y^2 = x^3 - 1386747*x + 368636886 over Rational Field sage: e.torsion_order() 16 sage: G = e.torsion_subgroup() sage: G Torsion Subgroup isomorphic to Multiplicative Abelian Group isomorphic to C2 x C8 associated to the Elliptic Curve defined by y^2 = x^3 - 1386747*x + 368636886 over Rational Field sage: G.0 (1227 : 22680 : 1) sage: G.1 (282 : 0 : 1) sage: list(G) [1, P1, P1^2, P1^3, P1^4, P1^5, P1^6, P1^7, P0, P0*P1, P0*P1^2, P0*P1^3, P0*P1^4, P0*P1^5, P0*P1^6, P0*P1^7] --~--~---------~--~----~------------~-------~--~----~ 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://sage.math.washington.edu/sage/ and http://sage.scipy.org/sage/ -~----------~----~----~----~------~----~------~--~---
