Algebraic functional equations and completely faithful Selmer groups

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Let E be an elliptic curve---defined over a number field K---without complex multiplication and with good ordinary reduction at all the primes above a rational prime p ≥ 5. We construct a pairing on the dual p∞-Selmer group of E over any strongly admissible p-adic Lie extension K∞/K under the assumption that it is a torsion module over the Iwasawa algebra of the Galois group G=Gal(K∞/K). Under some mild additional hypotheses this gives an algebraic functional equation of the conjectured p-adic L-function. As an application we construct completely faithful Selmer groups in case the p-adic Lie extension is obtained by adjoining the p-power division points of another non-CM elliptic curve A.