Using the reduction theory of Nrron we give necessary conditions for the existence of points of order q on elliptic curves E rational over global fields. An application is the determination of all elliptic cu rves /Q with integer j and torsion points, generalizing Olson [8]. Another application is a theorem about semistable reduction whose consequences generalize a theorem of Olson [9] ( K = Q) and give divisibility conditions for the discriminant and the coefficients of E related with the paper of Zimmer [13] as well as "diophantine" equations related with Fermat's equation that are discussed for K Q and K a function field. We are interested in elliptic curves over global fields K (i.e. : K is a finite number field or K is a function field of one variable over a finite field) and especially in the torsion group of E(K), where E(K) is the group of K-rational points of E. It is well known that E(K) is finitely generated, it is conjectured that if K is a number field then the order of the torsion group of E(K) is bounded by some number depending only on K (cf. Demjanenko [1]). In any case in order to handle with E(K) the first step is to determine the torsion group. In principle this is not so difficult; if one uses the results of Lutz [6] and Zimmer [13], one sees immediately that for every E there exist points of q-power-order only for a finite number of primes q, as the equations for points of order q are known (in principle) one has only t ~ test what orders really occur. But as the computational work grows very rapidly with q it is usefull to look for sharper necessary conditions, and this shall be done in this paper.