13.1 Conductor

How do you compute the conductor of an elliptic curve (over $ \mathbb{Q}$ ) in Sage?

Once you define an elliptic curve $ E$ in Sage, using the EllipticCurve command, the conductor is one of several ``methods'' associated to $ E$ . Here is an example of the syntax (borrowed from section 2.4 ``Modular forms'' in the tutorial):

sage: E = EllipticCurve([1,2,3,4,5])
sage: E
Elliptic Curve defined by y^2 + x*y + 3*y = x^3 + 2*x^2 + 4*x + 5 over 
Rational Field
sage: E.conductor()
10351

See About this document... for information on suggesting changes.