Period computations for covers of elliptic curves

Rubinstein-Salzedo, Simon

doi:10.1090/S0025-5718-2014-02797-X

Period computations for covers of elliptic curves
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by Simon Rubinstein-Salzedo;

Math. Comp. 83 (2014), 2455-2470

DOI: https://doi.org/10.1090/S0025-5718-2014-02797-X

Published electronically: January 13, 2014

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Abstract:

In this article, we construct algebraic equations for a curve $C$ and a map $f$ to an elliptic curve $E$, with pre-specified branching data. We do this by determining certain relations that the periods of $C$ and $E$ must satisfy and using these relations to approximate the coefficients to high precision. We then conjecture which algebraic numbers the coefficients are, and then we prove this conjecture to be correct.

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