Local Torsion on Elliptic Curves

Let E be an elliptic curve over Q . 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 Qp , 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 Qp .;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 Q .