1 research outputs found
Distorting the volcano
Volcanoes of ℓ–isogenies of elliptic curves are a special case of graphs
with a cycle called crater. In this paper, given an elliptic curve E of a
volcano of ℓ–isogenies, we present a condition over an endomorphism ϕ of
E in order to determine which ℓ–isogenies of E are non-descending. The
endomorphism ϕ is defined as the crater cycle of an m–volcano where E
is located, with m 6= â„“. The condition is feasible when Ï• is a distortion
map for a subgroup of order â„“ of E. We also provide some relationships
among the crater sizes of volcanoes of m–isogenies whose elliptic curves
belong to a volcano of ℓ–isogenies.Research of the authors was partially supported by grants MTM2013-46949-P (Spanish MINECO) and 2014 SGR1666 (Generalitat de Catalunya)