Infinitely many pairs of non-isomorphic elliptic curves sharing the same BSD invariants
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arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866918128474128384 |
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| author | Shiga, Asuka |
| author_facet | Shiga, Asuka |
| contents | We prove that there exist infinitely many pairs of non-isomorphic elliptic curves over $\mathbb{Q}$ sharing the same BSD invariants -- including their Mordell--Weil groups, Tate--Shafarevich groups, Tamagawa numbers, regulators, and real periods -- and their Kodaira symbols and minimal discriminants, while having distinct $j$-invariants. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_18574 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Infinitely many pairs of non-isomorphic elliptic curves sharing the same BSD invariants Shiga, Asuka Number Theory We prove that there exist infinitely many pairs of non-isomorphic elliptic curves over $\mathbb{Q}$ sharing the same BSD invariants -- including their Mordell--Weil groups, Tate--Shafarevich groups, Tamagawa numbers, regulators, and real periods -- and their Kodaira symbols and minimal discriminants, while having distinct $j$-invariants. |
| title | Infinitely many pairs of non-isomorphic elliptic curves sharing the same BSD invariants |
| topic | Number Theory |
| url | https://arxiv.org/abs/2507.18574 |