Ok, that's very helpful. Thank you very much. Best regards.
On 17 sep, 15:26, Craig Citro <[email protected]> wrote: > > Actually, I wonder if there is some list of the usual commands to use > > on Elliptic Curves. I've been searching for it, but I only found the > > commands to define an Elliptic Curve (just over Q or a finite field, > > but not over a function field, say Q(t) for example) and operate with > > some of points in it. I would like to do other things and I don't > > really know how to. Sorry to bother. Thanks. > > Hi, > > Most of the available commands are methods on an elliptic curve > object. You can use tab completion to see what all is available: > > sage: E = EllipticCurve('11a') > sage: E.<tab> > > and a huge list of options will pop out. (Here the "<tab>" means hit > tab. This also works in the notebook.) Once you find one you want, you > can use ? to see some documentation, and ?? to see the source: > > sage: E.tamagawa_number? > Type: instancemethod > Base Class: <type 'instancemethod'> > String Form: <bound method > EllipticCurve_rational_field.tamagawa_number of Elliptic Curve defined > by y^2 + y = x^3 - x^2 - 10*x - 20 over Rational Field> > Namespace: Interactive > File: > /sage/local/lib/python2.5/site-packages/sage/schemes/elliptic_curves/ell_rational_field.py > Definition: E.tamagawa_number(self, p) > Docstring: > > The Tamagawa number of the elliptic curve at `p`. > > This is the order of the component group > `E(QQ_p)/E^0(QQ_p)`. > > EXAMPLES:: > > sage: E = EllipticCurve('11a') > sage: E.tamagawa_number(11) > 5 > sage: E = EllipticCurve('37b') > sage: E.tamagawa_number(37) > 3 > > sage: E.tamagawa_number?? > Type: instancemethod > Base Class: <type 'instancemethod'> > String Form: <bound method > EllipticCurve_rational_field.tamagawa_number of Elliptic Curve defined > by y^2 + y = x^3 - x^2 - 10*x - 20 over Rational Field> > Namespace: Interactive > File: > /sage/local/lib/python2.5/site-packages/sage/schemes/elliptic_curves/ell_rational_field.py > Definition: E.tamagawa_number(self, p) > Source: > def tamagawa_number(self, p): > r""" > The Tamagawa number of the elliptic curve at `p`. > > This is the order of the component group > `E(\QQ_p)/E^0(\QQ_p)`. > > EXAMPLES:: > > sage: E = EllipticCurve('11a') > sage: E.tamagawa_number(11) > 5 > sage: E = EllipticCurve('37b') > sage: E.tamagawa_number(37) > 3 > """ > return self.local_data(p).tamagawa_number() > > Hope that gets you started ... > > -cc --~--~---------~--~----~------------~-------~--~----~ 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 -~----------~----~----~----~------~----~------~--~---
