Title

A Brief Exploration of Rational Points on Elliptic Curves

Date

5-31-2018 2:00 PM

End Time

31-5-2018 2:20 PM

Location

HWC 204

Session Chair

Cheryl Beaver

Session Chair

Leanne Merrill

Session Title

Mathematics Capstone Project Presentations

Presentation Type

Presentation

Faculty Sponsor(s)

Leanne Merrill

Abstract

Combining abstract algebra, algebraic geometry and number theory, the study of elliptic curves can yield interesting results and applications. Though the subject can become very involved, we provide an introduction to the study of elliptic curves and the group of rational points on elliptic curves. We derive and prove the structure of the group of rational points on elliptic curves, adhering to the work of Silverman and Tate, and prove that the group operation is Abelian. We also consider the work of Rienzo by working out examples over finite fields. We explore the general geometric structure of elliptic curves, Weierstrass normal form and the different types of curves associated with the Weierstrass form of a curve, and finally, provide a possible proof of the conjecture given by Rienzo in "Elliptic Curves Over Local Fields."

This document is currently not available here.

Share

COinS
 
May 31st, 2:00 PM May 31st, 2:20 PM

A Brief Exploration of Rational Points on Elliptic Curves

HWC 204

Combining abstract algebra, algebraic geometry and number theory, the study of elliptic curves can yield interesting results and applications. Though the subject can become very involved, we provide an introduction to the study of elliptic curves and the group of rational points on elliptic curves. We derive and prove the structure of the group of rational points on elliptic curves, adhering to the work of Silverman and Tate, and prove that the group operation is Abelian. We also consider the work of Rienzo by working out examples over finite fields. We explore the general geometric structure of elliptic curves, Weierstrass normal form and the different types of curves associated with the Weierstrass form of a curve, and finally, provide a possible proof of the conjecture given by Rienzo in "Elliptic Curves Over Local Fields."