2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/106419Let E be an elliptic curve defined over the rationals and let N be its conductor. Assume N is prime. In this paper we give numerical evidence that suggests some conjectures on the 2-divisibility of certain sums of Heenger points on E of discriminant D dividing 4N. One of these conjectures suggests a possible link between the parity of the eigenvalue a_A(2) and the parity of the Shafarevich-Tate group of certain elliptic curves A of square conductor.10 pages, 3 tablesNumber Theory11G05; 11G40text