Graduation Year

Spring 2013

Document Type

Open Access Senior Thesis

Degree Name

Bachelor of Arts

Department

Mathematics

Reader 1

Christopher Towse

Reader 2

Dagan Karp

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© 2013 Tracy Layden

Abstract

This thesis examines the rank of elliptic curves. We first examine the correspondences between projective space and affine space, and use the projective point at infinity to establish the group law on elliptic curves. We prove a section of Mordell’s Theorem to establish that the abelian group of rational points on an elliptic curve is finitely generated. We then use homomorphisms established in our proof to find a formula for the rank, and then provide examples of computations.

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Number Theory Commons

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