  Let $E$ be an elliptic curve defined over $\mathbb Q$. Let $\Gamma$ be a
subgroup of $E(\mathbb Q)$ and $P\in E(\mathbb Q)$. In [1], it was proved that
if $E$ has no nontrivial rational torsion points, then $P\in\Gamma$ if and only
if $P\in \Gamma$ mod $p$ for finitely many primes $p$. In this note, assuming
the General Riemann Hypothesis, we provide an explicit upper bound on these
primes when $E$ does not have complex multiplication and either $E$ is a
semistable curve or $E$ has no exceptional prime.
