Periods of Hilbert modular forms and rational points on elliptic curves

@inproceedings{Darmon2003PeriodsOH,
  title={Periods of Hilbert modular forms and rational points on elliptic curves},
  author={Henri Darmon and Adam Logan},
  year={2003}
}
Let E be a modular elliptic curve over a totally real field. Chapter 8 of [Dar2] formulates a conjecture allowing the construction of canonical algebraic points on E by suitably integrating the associated Hilbert modular form. The main goal of the present work 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. 

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