A Banach space X is superreflexive if each Banach space Y that is finitely
representable in X is reflexive. Superreflexivity is known to be equivalent to
J-convexity and to the non-existence of uniformly bounded factorizations of the
summation operators S_n through X. We give a quantitative formulation of this
equivalence. This can in particular be used to find a factorization of S_n
through X, given a factorization of S_N through [L_2,X], where N is `large'
compared to n