On several families of elliptic curves with arbitrary large Selmer groups

Fei Li, Derong Qiu

In this paper, we calculate the $\varphi (\hat{\varphi })-$Selmer groups $ S^{(ϕ)} (E / \Q) $ and $ S^{(\hatφ)} (E^{\prime} / \Q) $ of elliptic curves $y^2=x(x+\epsilon pD)(x+\epsilon qD)$ via desc…