On elliptic units and p-adic Galois representations attached to elliptic curves Original Research Article

Let K be a quadratic imaginary number field with discriminant DK≠-3,-4 and class number one. Fix a prime pgreater-or-equal, slanted7 which is not ramified in K and write hp for the class number of the ray class field of K of conductor p. Given an elliptic curve A/K with complex multiplication by K, let image be the representation which arises from the action of Galois on the Tate module. Herein it is shown that if image then the image of a certain deformation image of image is “as big as possible”, that is, it is the full inverse image of a Cartan subgroup of image. The proof rests on the theory of Siegel functions and elliptic units as developed by Kubert, Lang and Robert.