Mordell’s theorem,which says that the group of rational points on an elliptic curve is finitelygenerated;

a special case of Hasse’s theorem, due to Gauss, which de-scribes the number of points on an elliptic curve defined over a finite field.

Nagell–Lutz theorem, which gives a precise procedure for finding all of therational points of finite order on an elliptic curve;

the emphasis of this book is on number theoretic aspects ofelliptic curves, so we feel that an informal approach to the underlying geom-etry is permissible, since it allows us more rapid access to the number theory.