Original scientific paper

https://doi.org/10.3336/gm.47.2.03

A remark on the injectivity of the specialization homomorphism

Ivica Gusić ; Faculty of Chemical Engin. and Techn., University of Zagreb, Marulićev trg 19, 10000 Zagreb, Croatia
Petra Tadić ; Geotechnical faculty, University of Zagreb, Hallerova aleja 7, 42000 Varaždin, Croatia

Abstract

Let E:y2=(x-e1)(x-e2)(x-e3), be a nonconstant elliptic curve over Q(T). We give sufficient 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.

Keywords

Elliptic curve; specialization homomorphism; rank; generators

Hrčak ID:

93940

URI

https://hrcak.srce.hr/93940

Publication date:

19.12.2012.

Visits: 848 *