Open Access Senior Thesis
Bachelor of Arts
© 2013 Tracy Layden
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.
Layden, Tracy, "Factoring the Duplication Map on Elliptic Curves for use in Rank Computations" (2013). Scripps Senior Theses. 342.