engleski

A remark on the injectivity of the specialization homomorphism

Let E : y^2 = (x - e1)(x - e2)(x - e3) be a nonconstant elliptic curve over Q(T). We give sucient conditions for a specialization homomorphism to be injective, based on the unique factorization in Z[T] and Z. The result is applied for calculating exactly the Mordell-Weil group of several elliptic curves over Q(T) coming from a paper by Rubin and Silverberg.

elliptic curve; specialization homomorphism; rank; generators

nije evidentirano