Three-isogeny Selmer groups and ranks of abelian varieties in quadratic twist families over a number field

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

For an abelian variety $A$ over a number field $F$, we prove that the average rank of the quadratic twists of $A$ is bounded, under the assumption that the multiplication-by-3 isog…