Abstract
Let $E$ be an elliptic curve defined over a global field $K$. By a global field $K$ we mean an algebraic number fieldor an algebraic function field of one variable over a field $k$ as its field of constants. For technical reasonwe may assume that our function field has characteristic $\neq 2$.Our main interest is to compute torsion points of $E$ over $K$. In this paper we provide two methods. One isto use division polynomials, and the other is to use the generalized Nagell-Lutz theorem.