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To prove the BSD conjecture, one has to know about 'the finiteness of the Shafarevich Tate group'. But, an example of an elliptic curve of rank 2 (whose Sha group $III(E/\mathbb{Q})$ Ш(E/\mathbb{Q})$is finite) is not yet known. Is there any example of an elliptic curve of rank 2 such that$p$-primary components of$III$Ш are trivial for$p$outside a finite set of primes?. In particular,$III(E/\mathbb{Q})[p]$Ш(E/\mathbb{Q})[p]$ is trivial for $p$ $\neq$ 2, 3, 5, 7.

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# Order of 'Sha'.Ш(Sha)

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To prove the BSD conjecture, one has to know about 'the finiteness of the Shafarevich Tate group'. But, an example of an elliptic curve of rank 2 (whose Sha group $III(E/\mathbb{Q})$ is finite) is not yet known.

Is there any example of an elliptic curve of rank 2 such that $p$-primary components of $III$ are trivial for $p$ outside a finite set of primes?. In particular, $III(E/\mathbb{Q})[p]$ is trivial for $p$ $\neq$ 2, 3, 5, 7.

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