$2$-adic Representations of Elliptic Curves over $\mathbb{Q}_2$

We provide a complete classification of the rational $2$ -adic Tate modules $V_{2} (E)$ of elliptic curves $E / Q_{2}$ with potentially good reduction. The classification is given in terms of the filtered $(φ, G a l)$ -modules associated to $V_{2} (E)$ via Fontaine’s functor $D_{p c r i s}^{*}$ .

$2$ -adic Representations of Elliptic Curves over $Q_{2}$

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$2$ -adic Representations of Elliptic Curves over $Q_{2}$

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22-adic Representations of Elliptic Curves over Q2Q2​

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22-adic Representations of Elliptic Curves over Q2Q2​

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$2$ -adic Representations of Elliptic Curves over $Q_{2}$

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$2$ -adic Representations of Elliptic Curves over $Q_{2}$

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