Glasnik Matematicki, Vol. 47, No. 2 (2012), 265-275.

A REMARK ON THE INJECTIVITY OF THE SPECIALIZATION HOMOMORPHISM

Ivica Gusić and Petra Tadić

Faculty of Chemical Engin. and Techn., University of Zagreb, Marulićev trg 19, 10000 Zagreb, Croatia
e-mail: igusic@fkit.hr

Geotechnical faculty, University of Zagreb, Hallerova aleja 7, 42000 Varaždin, Croatia
e-mail: petra.tadic.zg@gmail.com, ptadic@gfv.hr

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.

2010 Mathematics Subject Classification.   11G05, 14H52.

Key words and phrases.   Elliptic curve, specialization homomorphism, rank, generators.

Full text (PDF) (free access)

DOI: 10.3336/gm.47.2.03

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