Mordell's theorem and the group law for Q-rational elliptic curves

Sammanfattning

We give an introduction to elliptic curves with rational or complex coefficients and their group law. On elliptic curves over Q, the rational points form a subgroup. We explain why the Q-rational elliptic curves are isomorphic to elliptic curves on Weierstrass normal form. We eventually prove Mordell’s theorem which states that, in case of a rational point of order 2, the group of rational points on a Q-rational elliptic curve is finitely generated.