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Mar 17, 2016 at 20:15 vote accept Robert
Mar 17, 2016 at 20:11 comment added Chris Wuthrich Yes, they don't assume anything on $E$. It has more to do with the shape of the image of the global Galois representation on $T_pE$ rather than how this looks locally at $p$. In particular their proof splits up according to whether $E$ has cm or not.
Mar 17, 2016 at 20:09 comment added Robert Is it true if $E$ has supersingular reduction at $p$ ?
Mar 17, 2016 at 20:07 history answered Chris Wuthrich CC BY-SA 3.0