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Let $E,E'$ be a pair of elliptic curves defined over $\mathbb{Z}$. Let $T_p[E], T_p[E']$ be their associated ($p$-adic) Tate modules. These are Galois representations for the absolute Galois group of $...

Let $E/Q$ be an elliptic curve. $E(\bar{Q})$ is a complicated abelian group, which equals to all closed points of $\bar{E}$, and also, a $G_Q$-Galois module. Its torsion part, $E(\bar{Q})_{tor}$ is a ...