Weber modular curves and modular isogenies
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866918420547633152 |
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| author | Colò, Leonardo Kohel, David |
| author_facet | Colò, Leonardo Kohel, David |
| contents | We study the modular curves defined by Weber functions, and associated modular polynomials, action of $\mathrm{SL}_2(\mathbb{Z})$, and parametrizations of elliptic curves with a view to the study of the isogeny graphs that they determine, particularly for supersingular elliptic curves. In addition to applications to efficient isogeny computation in cryptographic applications, we present an application to explicit Galois representations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_29802 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Weber modular curves and modular isogenies Colò, Leonardo Kohel, David Number Theory We study the modular curves defined by Weber functions, and associated modular polynomials, action of $\mathrm{SL}_2(\mathbb{Z})$, and parametrizations of elliptic curves with a view to the study of the isogeny graphs that they determine, particularly for supersingular elliptic curves. In addition to applications to efficient isogeny computation in cryptographic applications, we present an application to explicit Galois representations. |
| title | Weber modular curves and modular isogenies |
| topic | Number Theory |
| url | https://arxiv.org/abs/2603.29802 |