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In particular, for the curve $E = X_0(49)$ we prove the following results. Let $q_1, \\ldots, q_r$ be distinct primes which are congruent to $1$ modulo $4$ and inert in the field $F = \\mathbb Q(\\sqrt{-7})$, and let $E^{(R)}$ be the twist of $E$ by the quadratic extension $\\mathbb Q(\\sqrt{R})/\\mathbb Q$, where $R=q_1\\ldots q_r$. 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In particular, for the curve $E = X_0(49)$ we prove the following results. Let $q_1, \\ldots, q_r$ be distinct primes which are congruent to $1$ modulo $4$ and inert in the field $F = \\mathbb Q(\\sqrt{-7})$, and let $E^{(R)}$ be the twist of $E$ by the quadratic extension $\\mathbb Q(\\sqrt{R})/\\mathbb Q$, where $R=q_1\\ldots q_r$. 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