On Elliptic Curves

Author

Montana S. Miller, Missouri State UniversityFollow

Date of Graduation

Spring 2021

Degree

Master of Natural and Applied Science in Mathematics

Department

Mathematics

Committee Chair

Kishor Shah

Abstract

An elliptic curve over the rational numbers is given by the equation y² = x³+Ax+B. In our thesis, we study elliptic curves. It is known that the set of rational points on the elliptic curve form a finitely generated abelian group induced by the secant-tangent addition law. We present an elementary proof of associativity using Maple. We also present a relatively concise proof of the Mordell-Weil Theorem.

Keywords

elliptic curves, plane curves, associativity, groups, Mordell, Weil, Fermat, Andrew Wiles, Maple

Subject Categories

Algebra | Algebraic Geometry | Number Theory

Copyright

© Montana S. Miller

Recommended Citation

Miller, Montana S., "On Elliptic Curves" (2021). MSU Graduate Theses. 3604.
https://bearworks.missouristate.edu/theses/3604