A Constructive Proof of Massers Theorem

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{ leftvert c_{4}^{3}rightvert,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{ leftvert c_{4}^{3}rightvert,c_{6}^{2}right} $. Masser showed that there are infinitely many good Frey curves. Here we give a constructive proof of this assertion.