Distinct differences of singular moduli
Fuente:
arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866909551980183552 |
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| author | Fowler, Guy Tron, Emanuele |
| author_facet | Fowler, Guy Tron, Emanuele |
| contents | Let $E_1, E_2 / \mathbb{C}$ be non-isomorphic elliptic curves with complex multiplication. We prove that the pair $(E_1, E_2)$ is characterised, up to isomorphism, by the difference $j(E_1) - j(E_2)$ of the respective $j$-invariants. In other words, we show that if $x_1, x_2, x_3, x_4$ are singular moduli such that $x_1 - x_2 = x_3 - x_4$, then either $(x_1, x_2) = (x_3, x_4)$ or $(x_1, x_3) = (x_2, x_4)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_19686 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Distinct differences of singular moduli Fowler, Guy Tron, Emanuele Number Theory Algebraic Geometry 11G18, 14G35 Let $E_1, E_2 / \mathbb{C}$ be non-isomorphic elliptic curves with complex multiplication. We prove that the pair $(E_1, E_2)$ is characterised, up to isomorphism, by the difference $j(E_1) - j(E_2)$ of the respective $j$-invariants. In other words, we show that if $x_1, x_2, x_3, x_4$ are singular moduli such that $x_1 - x_2 = x_3 - x_4$, then either $(x_1, x_2) = (x_3, x_4)$ or $(x_1, x_3) = (x_2, x_4)$. |
| title | Distinct differences of singular moduli |
| topic | Number Theory Algebraic Geometry 11G18, 14G35 |
| url | https://arxiv.org/abs/2503.19686 |