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Contributions to the arithmetic of elliptic curves Ingram, Patrick M.

Abstract

We present various published and unpublished results on elliptic curves. In particular, we focus on the torsion structures of elliptic curves, and how this is, influenced by the relative sizes of the coefficients. We see in the final chapter that these results axe special cases of a more general result on approximating rational numbers j-invariants of elliptic curves with certain structures. Various other results regarding the divisibility properties (and consequently integrality) of rational points on elliptic curves are also discussed.

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