Homomorphisms From the Group of Rational Points On Elliptic Curves to Class Groups of Quadratic Number Fields Original Research Article

The main purpose of this paper is to prove that there is a homomorphism from the group of primitive points on an elliptic curve given by an equation Y2 = X3 + a2X2 + a4X + a6 to the ideal class group of the order image + image [formula]. Two applications are given. First we prove a conjecture concerning the order of ideals coming from rational points of infinite order on the curve. Then we describe how to construct families of quadratic number fields containing a subgroup of the ideal class group isomorphic to the torsion group of the curve.