There exist infinitely many pairs of non-isomorphic elliptic curves over Q with identical BSD data, and this remains true when equality of Kodaira symbols and minimal discriminants is imposed.
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Infinitely many pairs of non-isomorphic elliptic curves sharing the same BSD invariants
There exist infinitely many pairs of non-isomorphic elliptic curves over Q with identical BSD data, and this remains true when equality of Kodaira symbols and minimal discriminants is imposed.