We provide an upper bound for the ranks of quadratic twists of abelian varieties over number fields with no 2-torsion points over the base field. This is analogous to a classical result on the the ranks of elliptic curves over \(\mathbb {Q}\) with full rational 2-torsion in the setting of quadratic twist families, as well as the Brumer-Kramer rank bound for elliptic curves given in [5] considered in the setting of quadratic twist families. We give a refinement to this bound in the case of elliptic curves. As applications of this refinement, we provide lower bounds for the 2-Selmer ranks of quadratic twists, and provide an example of an elliptic curve with the following property: all but at most finitely many of its prime twists have strictly positive 2-Selmer rank. As a further application, we present a general method for generating infinite families of rank-0 twists of elliptic curves.
