Abstract Let p be an odd prime, and let E₁ and E₂ be two elliptic curves defined over a number field K, with good ordinary reduction at p. We compare the -ranks and (generalized) Iwasawa invariants of the Pontryagin duals of the Selmer groups of E₁ and E₂ over Zₚᵈ -extensions L_ of K for general d 1 under the hypothesis that E₁pⁱ E₂pⁱ as Galois modules for a sufficiently large i. This generalizes and complements previous work over Zₚ -extensions. The comparison of generalized Iwasawa invariants is related via an up-down approach to the comparison of the variation of classical Iwasawa invariants over the Zₚ -extensions of K which are contained in L_.
Kleine et al. (Mon,) studied this question.