On several families of elliptic curves with arbitrary large Selmer groups

In this paper, we calculate the $\phi (\hat{\phi})-$Selmer groups $S^{(\phi)} (E / \Q)$ and $S^{(\hat{\varphi})} (E^{\prime} / \Q)$ of elliptic curves $y^{2} = x (x + \epsilon p D) (x + \epsilon q D)$ via descent theory (see [S, Chapter X]), in particular, we obtain that the Selmer groups of several families of such elliptic curves can be arbitrary large.