Date of Award
Bachelor of Science
elliptic curves, torsion points, torsion subgroup, torsion group, torsion, nagell, lutz, weierstrass, algebraic geometry, number theory
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.
Porat, Zachary, "Classification of Torsion Subgroups for Mordell Curves" (2020). Honors Theses. 2367.