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Let $ E$ be an elliptic curve over $ \mathbb{Q}_p$ . I was told that if $ F$ is the smallest Galois extension over $ \mathbb{Q}_p$ then the inertia subgroup $ I_{v’}$ of $ G_{F/\mathbb{Q}_p}$ is a subgroup of the automorphism group of $ \widetilde{E}$ . Here $ \widetilde{E}$ is the elliptic curve reduced modRead more