Periods of Hilbert modular forms and rational points on elliptic curves

Abstract

Let E be a modular elliptic curve over a totally real field. A conjecture of the first author allows the construction of canonical algebraic points on E by suitably integrating the associated Hilbert modular form. The main goal of the present paper is to obtain numerical evidence for this conjecture in the first case where it asserts something nontrivial, namely, when E has everywhere good reduction over a real quadratic field.