Building on the p-adic conservation law for BSD invariants (DOI: 10. 5281/zenodo. 19534362), we conduct a systematic computational study of how Birch and Swinnerton-Dyer invariants behave under isogeny, using the full Cremona database (2, 483, 649 elliptic curves, conductor ≤ 500, 000). Principal findings: (1) |Sha|·D is constant within every isogeny class (545, 784 classes, zero exceptions) ; (2) Selmer saturation rate increases from 28% at rank 0 to 100% at rank 2; (3) |Sha|=1 for all 6, 680 curves of rank ≥ 3; (4) Pr (vₚ (|Sha|) varies) ~ 1/p⁴; (5) the 21 rank-2 exceptions are completely characterized. Includes 19 verification scripts.
Tao Rui (Sun,) studied this question.