Selmer groups of families of elliptic curves with an $\mathrm{\ell }$-isogeny

For certain families of elliptic curves admitting a rational isogeny of prime degree $\mathrm{\ell }$, we establish a central limit theorem for the Tamagawa ratio and derive bounds on its average value. By using the Tamagawa ratio to bound the size of the $\mathrm{\ell }$-isogeny Selmer group from below, we show that for $\mathrm{\ell }\in \{2,3,5,7,13\}$, there exist elliptic curves with arbitrarily large $\mathrm{\ell }$-Selmer groups.