this talk is about a long-term project to verify the full birch and swinnerton-dyer conjecture for every elliptic curve in cremona's book, except the $18$ optimal curves of rank $2$. the methods involve kolyvagin's euler system of heegner points, computation, and whatever else one can use. i'll begin with a discussion of the birch and swinnerton-dyer conjecture for elliptic curves, and methods for computing the true order of shafarevich-tate groups, along with frustrating difficulties that have yet to be overcome.