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Volcanoes of l-isogenies of elliptic curves over finite fields: the case l=3

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PJTN05_08.pdf (196.3Kb)
Issue date
2007
Author
Miret, Josep M. (Josep Maria)
Sadornil Renedo, Daniel
Tena Ayuso, Juan
Tomàs Cuñat, Rosa Ana
Valls Marsal, Magda
Suggested citation
Miret, Josep M. (Josep Maria); Sadornil Renedo, Daniel; Tena Ayuso, Juan; Tomàs Cuñat, Rosa Ana; Valls Marsal, Magda; . (2007) . Volcanoes of l-isogenies of elliptic curves over finite fields: the case l=3. Publicacions matemàtiques, 2007, vol. Extra, p. 165-180. https://doi.org/10.5565/PUBLMAT_PJTN05_08.
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Abstract
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.
URI
http://hdl.handle.net/10459.1/44520
DOI
https://doi.org/10.5565/PUBLMAT_PJTN05_08
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Publicacions matemàtiques, 2007, vol. Extra, p. 165-180
European research projects
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  • Articles publicats (Matemàtica) [266]

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