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Fix a prime $p$. If two elliptic curves over $\mathbb{Q}$ have the same p-adic Galois representation, then what relatinships do we know between them? Any references are welcome.

If two elliptic curves over $\mathbb{Q}$ have the same p-adic Galois representation, then what relatinships do we know between them? Any references are welcome.

Fix a prime $p$. If two elliptic curves over $\mathbb{Q}$ have the same p-adic Galois representation, then what relatinships do we know between them? Any references are welcome.

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Bonbon
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If two elliptic curves over $\mathbb{Q}$ have the same p-adic Galois representation, then what relatinships do we know between them? Any references are welcome.

If two elliptic curves over $\mathbb{Q}$ have the same Galois representation, then what relatinships do we know between them? Any references are welcome.

If two elliptic curves over $\mathbb{Q}$ have the same p-adic Galois representation, then what relatinships do we know between them? Any references are welcome.

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Bonbon
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Elliptic curves with the same Galois representation

If two elliptic curves over $\mathbb{Q}$ have the same Galois representation, then what relatinships do we know between them? Any references are welcome.