Tamagawa Numbers of Elliptic Curves with an $\mathrm{\ell }$-isogeny

Let $\mathrm{\ell }$ be an odd prime, and suppose $E$ is an elliptic curve defined over the rational numbers $\mathbb{Q}$. If $E$ has an $\mathrm{\ell }$-torsion point, then there has been significant work done on characterizing the $\mathrm{\ell }$-divisibility of the global Tamagawa number of $E$. In this paper, we consider elliptic curves that are $\mathrm{\ell }$-isogenous to elliptic curves with an $\mathrm{\ell }$-torsion point and study the $\mathrm{\ell }$-divisibility of their global Tamagawa numbers.