# Maarten Derickx

Number theory seminar on March 18, 2011 at 3:30pm in Padelford C401.

## Title

Torsion points on elliptic curves over number fields of small degree.

## Abstract

Merel has shown that if we ﬁx , then there are only ﬁnitely many primes occurring as the order of a torsion point on an elliptic curve where is a number ﬁeld of degree . Oesterle has proven that the largest such is smaller then . Both upper bounds use a criterion by Kammienny. In my talk I will show several variations on this criterion. I will also show how to bring down the bound for and using this criterion using a computer program based on William Steins work on .