Computing Periods of Cusp Forms and Modular Elliptic Curves

Abstract

We present an improved method of computing the periods of a newform for Γ₀(N), which converges faster than the method used in [Cremona 1992] (and originally in [Tlngley 1975]). We also present some shortcuts that speed up the process of computing all modular elliptic curves of a given conductor N. As an appl ication of these methods, we report on the extension of the systematic computation of modular elliptic curves to all conductors up to 5077.