Elements of given order in Tate-Shafarevich groups of abelian varieties in quadratic twist families

Manjul Bhargava, Zev Klagsbrun, Robert J. Lemke Oliver +1

Let $A$ be an abelian variety over a number field $F$ and let $p$ be a prime. Cohen-Lenstra-Delaunay-style heuristics predict that the Tate-Shafarevich group of $A_s$ should contai…