Computing isogenies from modular equations in genus two
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arXiv
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| Format: | Preprint |
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2020
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| _version_ | 1866929644708560896 |
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| author | Kieffer, Jean Page, Aurel Robert, Damien |
| author_facet | Kieffer, Jean Page, Aurel Robert, Damien |
| contents | We present an algorithm solving the following problem: given two genus 2 curves over a field k with isogenous Jacobians, compute such an isogeny explicitly. This isogeny can be either an l-isogeny or, in the real multiplication case, an isogeny with cyclic kernel; we require that k have large enough characteristic and that the curves be sufficiently generic. Our algorithm uses modular equations for these isogeny types, and makes essential use of an explicit Kodaira--Spencer isomorphism in genus 2. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2001_04137 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Computing isogenies from modular equations in genus two Kieffer, Jean Page, Aurel Robert, Damien Algebraic Geometry Number Theory We present an algorithm solving the following problem: given two genus 2 curves over a field k with isogenous Jacobians, compute such an isogeny explicitly. This isogeny can be either an l-isogeny or, in the real multiplication case, an isogeny with cyclic kernel; we require that k have large enough characteristic and that the curves be sufficiently generic. Our algorithm uses modular equations for these isogeny types, and makes essential use of an explicit Kodaira--Spencer isomorphism in genus 2. |
| title | Computing isogenies from modular equations in genus two |
| topic | Algebraic Geometry Number Theory |
| url | https://arxiv.org/abs/2001.04137 |