Abstract

Let E be an elliptic curve over [Special characters omitted.] . Let p be a prime of good reduction for E. We say that p is a local torsion prime if E has p -torsion over [Special characters omitted.] , and more generally, we say that p is a local torsion prime of degree d if E has p -torsion over an extension of degree d of [Special characters omitted.] . We study in this thesis local torsion primes by presenting numerical evidence, and by computing estimates for the number of local torsion primes on average over all elliptic curves over [Special characters omitted.]