Computing periods of cusp forms and modular elliptic curves

Abstract

We present an improved method of computing the periods of a newform for {\mathversion{normal}$\Gamma$}$_0(N)$, which converges faster than the method used in [Cremona 1992] (and originally in [Tingley 1975]). We also present some shortcuts that speed up the process of computing all modular elliptic curves of a given conductor $N$. As an application of these methods, we report on the extension of the systematic computation of modular elliptic curves to all conductors up to 5077.