On the integral points of elliptic curves

Abstract

In this thesis, we focus on developing and implementing algorithms to find integral points on elliptic curves and generating useful data, based on Mordell's correspondence between integral points on elliptic curves and binary quartic forms, and existing algorithms to solve Thue equations arising from this algorithm. We then generate data of integral points for all elliptic curves up to some height, and summarize the average number of integral points and curves with many integral points or large integral points.Science, Faculty ofMathematics, Department ofGraduat