On 15/01/2008, David Harvey <[EMAIL PROTECTED]> wrote:
>
>
> On Jan 15, 2008, at 4:54 PM, Robert Bradshaw wrote:
>
> > What about
> >
> > sage: K.<a> = NumberField(x^2 + x - (3^3-3))
> > sage: E = EllipticCurve('37a'); E
> > Elliptic Curve defined by y^2 + y = x^3 - x over Rational Field
> > sage: X = E.change_ring(K); X
> > Elliptic Curve defined by y^2 + y = x^3 + (-1)*x over Number Field in
> > a with defining polynomial x^2 + x - 24
>
> But I think John wants the curve to be still defined over the base
> field. If E/K is an elliptic curve, and L/K is a field extension, and
> P is in E(L), then you lose information if you base change the curve
> up to E/L and think of P as a point on E/L. For example P doesn't
> have any non-trivial galois conjugates any more. To retain these you
> need to "remember" that the curve is actually defined over K.
>David is right -- exactly what I want is to have points defined over the extension without changing the curve. John > david > > > > > -- John Cremona --~--~---------~--~----~------------~-------~--~----~ 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-devel URLs: http://sage.scipy.org/sage/ and http://modular.math.washington.edu/sage/ -~----------~----~----~----~------~----~------~--~---
