Division polynomials for arbitrary isogenies
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arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866914480630267904 |
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| author | Stange, Katherine E. |
| author_facet | Stange, Katherine E. |
| contents | Following work of Mazur-Tate and Satoh, we extend the definition of division polynomials to arbitrary isogenies of elliptic curves, including those whose kernels do not sum to the identity. In analogy to the classical case of division polynomials for multiplication-by-n, we demonstrate recurrence relations, identities relating to classical elliptic functions, the chain rule describing relationships between division polynomials on source and target curve, and generalizations to higher dimension (i.e., elliptic nets). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_15428 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Division polynomials for arbitrary isogenies Stange, Katherine E. Number Theory Cryptography and Security Algebraic Geometry Primary: 11G05 11B37 14H52 Secondary: 11B39 11R37 14K02 Following work of Mazur-Tate and Satoh, we extend the definition of division polynomials to arbitrary isogenies of elliptic curves, including those whose kernels do not sum to the identity. In analogy to the classical case of division polynomials for multiplication-by-n, we demonstrate recurrence relations, identities relating to classical elliptic functions, the chain rule describing relationships between division polynomials on source and target curve, and generalizations to higher dimension (i.e., elliptic nets). |
| title | Division polynomials for arbitrary isogenies |
| topic | Number Theory Cryptography and Security Algebraic Geometry Primary: 11G05 11B37 14H52 Secondary: 11B39 11R37 14K02 |
| url | https://arxiv.org/abs/2503.15428 |