Elliptic curves: parity phenomena

Algebraic Geometry and Number Theory Seminar

I will describe a number of unexplained arithmetic phenomena about rational points on elliptic curves that are predicted by the Birch-Swinnerton-Dyer conjecture. This will primarily be a survey and hopefully very light on technical details, although there will also be a couple of new examples. The latter are joint work with Lilybelle Cowland Kellock.