Title: A family of monogenic $S_4$ quartic fields arising from elliptic curves,
Abstract: We consider partial torsion fields (fields generated by a root of a division
polynomial) for elliptic curves. By analysing the reduction properties of
elliptic curves, and applying the Montes Algorithm, we obtain information about
the ring of integers. In particular, for the partial $3$-torsion fields for a
certain one-parameter family of non-CM elliptic curves, we describe a power
basis. As a result, we show that the one-parameter family of quartic $S_4$
fields given by $T^4 - 6T^2 - \alpha T - 3$ for $\alpha \in \mathbb{Z}$ such
that $\alpha \pm 8$ are squarefree, are monogenic.