Rational Points on Modular Elliptic Curves

This book surveys some recent developments in the arithmetic of modular elliptic curves. It places special emphasis on the construction of rational points on elliptic curves, the Birch and Swinnerton-Dyer conjecture, and the crucial role played by modularity in shedding light on these two closely re

The book surveys some recent developments in the arithmetic of modular elliptic curves. It places a special emphasis on the construction of rational points on elliptic curves, the Birch and Swinnerton-Dyer conjecture, and the crucial role played by modula

Elliptic curves; Modular forms; Heegner points on $X 0(N)$; Heegner points on Shimura curves; Rigid analytic modular forms; Rigid analytic modular parametrisations; Totally real fields; ATR points; Integration on $mathcal{H} ptimesmathcal{H}$; Kolyvagin's theorem; Bibliography