  The Modified Szpiro Conjecture, equivalent to the $abc$ Conjecture, states
that for each $\epsilon>0$, there are finitely many rational elliptic curves
satisfying $N_{E}^{6+\epsilon}<\max\!\left\{ \left\vert
c_{4}^{3}\right\vert,c_{6}^{2}\right\} $ where $c_{4}$ and $c_{6}$ are the
invariants associated to a minimal model of $E$ and $N_{E}$ is the conductor of
$E$. We say $E$ is a good elliptic curve if $N_{E}^{6}<\max\!\left\{ \left\vert
c_{4}^{3}\right\vert,c_{6}^{2}\right\} $. Masser showed that there are
infinitely many good Frey curves. Here we give a constructive proof of this
assertion.
