Xiaoyu Huang, Temple University
Recent work of Burungale, Skinner, Tian, and Wan established the first infinite families of quadratic twists of non-CM elliptic curves over Q for which the strong Birch-Swinnerton-Dyer conjecture is known to hold. In this talk, I will describe how their criteria can be described as an explicit algorithm and apply it to the elliptic curve data in the L-functions and Modular Forms Database (LMFDB), thereby identifying curves of conductor at most 500,000 that admit infinitely many quadratic twists satisfying strong BSD. I will also present numerical evidence related to a conjecture of Radziwill and Soundararajan predicting Gaussian behavior in the analytic order of the Shafarevich-Tate group, along with a systematic positive bias within the BSD-satisfying subfamily.