2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/111450The conjectures of Deligne, Be\uılinson, and Bloch-Kato assert that there should be relations between the arithmetic of algebro-geometric objects and the special values of their $L$-functions. We make a numerical study for symmetric power $L$-functions of elliptic curves, obtaining data about the validity of their functional equations, frequency of vanishing of central values, and divisibility of Bloch-Kato quotients.Accepted to ANTS-VIINumber Theorytext