Abstract: The quasiparallelogram law is a theorem governing in a quantitative way the group structure on elliptic curves. In short, the law rules that the so called height functions on the curve are almost quadratic forms. In this presentation, I will introduce the classical height functions and discuss effective quasiparallelogram laws on elliptic curves over number fields with short Weierstrass equations. This work is motivated by a problem about uniform estimates on nonsingular cubic curves.
Handledare: Per Salberger