Explicit p-adic Hodge theory for elliptic curves and non-split Cartan images

Matthew Bisatt, Lorenzo Furio, Davide Lombardo

Let $E/{\mathbb{Q}}_p$ be an elliptic curve whose mod $p$ Galois image is contained in the normaliser of a non-split Cartan. We classify the possible $p$-adic images of $E$ using too…