Multiples of integral points on elliptic curves

If E is a minimal elliptic curve defined over Z, we obtain a bound C, depending only on the global Tamagawa number of E, such that for any point P∈E(Q), nP is integral for at most one value of n>C. As a corollary, we show that if E/Q is a fixed elliptic curve, then for all twists E′ of E of sufficient height, and all torsion-free, rank-one subgroups Γ⊆E′(Q), Γ contains at most 6 integral points. Explicit computations for congruent number curves are included.