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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