Determination of elliptic curves by their adjoint p-adic L-functions

Fix p an odd prime. Let E   be an elliptic curve over QQ with semistable reduction at p. We show that the adjoint p-adic L-function of E evaluated at infinitely many integers prime to p completely determines up to a quadratic twist the isogeny class of E  . To do this, we prove a result on the determination of isobaric representations of GL(3,AQ)GL(3,AQ) by certain L-values of p-power twists.