On the 2-divisibility of certain Heenger points
Abstract
Let 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 aA(2) and the parity of the Shafarevich-Tate group of certain elliptic curves A of square conductor.
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