Abstract
An elliptic curve E/Q is said to be good if NE6<max{|c43|,c62} where NE is the conductor of E and c4 and c6 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(Q)tors≅T.