This is probably a really silly question, but I was wondering if someone could explain the Birch and Swinnerton-Dyer conjecture to me in a simple way. I've read a lot about it, but cannot understand it. Maybe posting here will help.
What I do understand is the concept of ranks on an elliptic curve; for ever point that generates an infinite number of points on the elliptic curve, it contributes 1 to the rank. Further, I know that Mordell proved that every elliptic curve must have a finite rank.
Finally, with regards to BSD, I understand that the conjecture says that the "analytic" way of computing the rank is the same as the "algebraic" way of computing the rank. But what I cannot seem to understand is what exactly is the analytic way of computing the rank, or the algebraic way.
If anyone wants to help me out, that would be much appreciated! Thanks!