Volcanoes of ℓ-isogenies of elliptic curves over finite fields
This paper is devoted to the study of the volcanoes of ℓ-isogenies of elliptic curves over a finite field, focusing on their height as well as on the location of curves across its different levels. The core of the paper lies on the relationship between the ℓ-Sylow subgroup of an elliptic curve and t...
| Autores: | , , , , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2007 |
| País: | España |
| Institución: | Universitat Autònoma de Barcelona |
| Repositorio: | Dipòsit Digital de Documents de la UAB |
| Idioma: | inglés |
| OAI Identifier: | oai:ddd.uab.cat:138508 |
| Acceso en línea: | https://ddd.uab.cat/record/138508 https://dx.doi.org/urn:doi:10.5565/PUBLMAT_PJTN05_08 |
| Access Level: | acceso abierto |
| Palabra clave: | Elliptic curves Finite fields Isogenies Volcanoes ℓ-Sylow subgroup Algorithms |
| Sumario: | This paper is devoted to the study of the volcanoes of ℓ-isogenies of elliptic curves over a finite field, focusing on their height as well as on the location of curves across its different levels. The core of the paper lies on the relationship between the ℓ-Sylow subgroup of an elliptic curve and the level of the volcano where it is placed. The particular case ℓ = 3 is studied in detail, giving an algorithm to determine the volcano of 3-isogenies of a given elliptic curve. Experimental results are also provided. |
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