Little has been implemented so far.
The modular form associated to the elliptic curve E over Q.
An elliptic curve E with associated modular form f, when f is a weight 2 newform on Gamma_0(N) with rational Fourier coefficients. When N<10000 the Cremona database is used. (When N>10000 I coded an algorithm for computing E, but it is currently not reasonable to expect my implementation to work at such high level.)
> M := ModularForms(Gamma0(389),2); > f := Newform(M,1); > Degree(f); 1 > E := EllipticCurve(f); > E; Elliptic Curve defined by y^2 + y = x^3 + x^2 - 2*x over Rational Field > Conductor(E); 389 > time s := PowerSeries(f,200); // faster because it knows the elliptic curve Time: 0.509