Volcanoes of l-isogenies of elliptic curves over finite fields: the case l=3
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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| Formato: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2007 |
| País: | España |
| Recursos: | Universitat de Lleida (UdL) |
| Repositorio: | Repositori Obert UdL |
| OAI Identifier: | oai:repositori.udl.cat:10459.1/44520 |
| Acesso em linha: | https://doi.org/10.5565/PUBLMAT_PJTN05_08 http://hdl.handle.net/10459.1/44520 |
| Access Level: | acceso abierto |
| Palavra-chave: | Elliptic curves Finite fields Isogenies Volcanoes Corbes el·líptiques Grups finits Nombres, Teoria algebraica de |
| Resumo: | 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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