  An elliptic curve $E$ over $\mathbb{Q}$ is said to be good if
$N_{E}^{6}<\max\!\left\{ \left\vert c_{4}^{3}\right\vert ,c_{6}^{2}\right\} $
where $N_{E}$ is the conductor of $E$ and $c_{4}$ and $c_{6}$ are the
invariants associated to a global minimal model of $E$. In this article, we
generalize Masser's Theorem on the existence of infinitely many good elliptic
curves with full $2$-torsion. Specifically, we prove via constructive methods
that for each of the fifteen torsion subgroups $T$ allowed by Mazur's Torsion
Theorem, there are infinitely many good elliptic curves $E$ with
$E\!\left(\mathbb{Q}\right) _{\text{tors}}\cong T$.
