2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/122909We present a deterministic algorithm that computes the zeta function of a nonsupersingular elliptic curve E over a finite field with p^n elements in time quasi-quadratic in n. An older algorithm having the same time complexity uses the canonical lift of E, whereas our algorithm uses rigid cohomology combined with a deformation approach. An implementation in small odd characteristic turns out to give very good results.14 pagesNumber TheoryAlgebraic Geometry14H52; 11G20text