Let $E/\mathbb{Q}$ be an elliptic curve. Recall that Szpiro's conjecture says that for every $\epsilon > 0$, there exists $C_\epsilon$ such that $ |\Delta_E| \leq C_\epsilon(N_E)^{6 + \epsilon}, $ where $\Delta_E$ is the minimal discriminant of $E$ and $N_E$ is the conductor of $E$.
One consequence of Szpiro's conjecture is Fermat's Last Theorem for sufficiently large exponents and the $ABC$-conjecture for the exponent $3/2$.
My question is are there any other known consequences of Szpiro's conjecture (references are appreciated)?
EDIT: Preferably a consequence of the Szpiro conjecture that is distinct from a consequence of the $ABC$-conjecture.