  We present here quantitative versions in 1 dimension of Faltings'theorem
according to which the set of the K-rational points (where K is a given number
field) of an abelian variety A definied over K, which are close (with respect
to a v-adic distance on K) to some K-subvariety X of A, but not belonging to X,
is finite. We treat more exactly the case where A is an elliptic curve and X is
reduced to a point of A and we give (in this case) explicit bounds for the
cardinal of the exceptional finite set. We consider also, more generally,
instead of only one place v of K, a finite set S of places of K and the
distance from the point of A to X taking into account of all places of S.
