Volcanoes of $\ell$-isogenies of elliptic curves over finite fields: the case $\ell=3^*$

J. M. Miret, D. Sadornil, J. Tena, R. Tomàs, M. Valls
2007 Publicacions matemàtiques  
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.
doi:10.5565/publmat_pjtn05_08 fatcat:wwnk4j2i55da5px66aelmzydge