Date of Award
3-2020
Document Type
Open Access
Degree Name
Bachelor of Science
Department
Mathematics
First Advisor
Jeffrey Hatley
Keywords
elliptic curves, torsion points, torsion subgroup, torsion group, torsion, nagell, lutz, weierstrass, algebraic geometry, number theory
Abstract
Elliptic curves are an interesting area of study in mathematics, laying at the intersection of algebra, geometry, and number theory. They are a powerful tool, having applications in everything from Andrew Wiles’ proof of Fermat’s Last Theorem to cybersecurity. In this paper, we first provide an introduction to elliptic curves by discussing their geometry and associated group structure. We then narrow our focus, further investigating the torsion subgroups of elliptic curves. In particular, we will examine two methods used to classify these subgroups. We finish by employing these methods to categorize the torsion subgroups for a specific family of elliptic curves known as Mordell curves.
Recommended Citation
Porat, Zachary, "Classification of Torsion Subgroups for Mordell Curves" (2020). Honors Theses. 2367.
https://digitalworks.union.edu/theses/2367
Included in
Algebra Commons, Algebraic Geometry Commons, Geometry and Topology Commons, Number Theory Commons