Title: On $p$-degree of elliptic curves,
Abstract: In this note we investigate the $p$-degree function of elliptic curves over
the field $\mathbb{Q}_p$ of $p$-adic numbers. The $p$-degree measures the least
complexity of a non-zero $p$-torsion point on an elliptic curve. We prove some
properties of this function and compute it explicitly in some special cases.