Graduation Year
2013
Document Type
Open Access Senior Thesis
Degree Name
Bachelor of Arts
Department
Mathematics
Reader 1
Christopher Towse
Reader 2
Dagan Karp
Terms of Use & License Information
Rights Information
© 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.
Recommended Citation
Layden, Tracy, "Factoring the Duplication Map on Elliptic Curves for use in Rank Computations" (2013). Scripps Senior Theses. 342.
https://scholarship.claremont.edu/scripps_theses/342
