The distribution of ℓ^{∞}-Selmer groups in degree ℓ twist families II

We continue the investigation of the distribution of ℓ ∞ \ell ^{\infty } -Selmer groups in degree ℓ \ell twist families of Galois modules over number fields begun by the author in [J. Amer. Math. Soc. 39-1 (2026), pp. 1–72]. Building off the work on higher Selmer groups in that part, we find conditions under which we can compute the distribution of the ℓ ∞ \ell ^{\infty } -Selmer groups for a given degree ℓ \ell twist family. Along the way, we show that the average rank in the quadratic twist family of any given abelian variety over a number field is bounded.