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UBC Theses and Dissertations

Elliptic curves of prime conductor - an exploration of conjecture, data and bias Hatziiliou, Andreas


This thesis presents data collected from the Bennett-Gherga-Retchnizer dataset of elliptic curves of prime conductor over the rationals. For these curves, we analyze the behaviors of the invariants which appear in the Birch and Swinnerton-Dyer conjecture - we present comparisons to the literature and point out differences and similarities between the families of elliptic curves of prime and composite conductors. Moreover, we present heuristic and computational evidence towards biases in the ranks, conductors and coefficients of elliptic curves within the latter family.

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