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Injectivity of the specialization homomorphism of elliptic curves (CROSBI ID 210338)

Prilog u časopisu | izvorni znanstveni rad | međunarodna recenzija

Gusić, Ivica ; Tadić, Petra Injectivity of the specialization homomorphism of elliptic curves // Journal of number theory, 148 (2015), 137-152. doi: 10.1016/j.jnt.2014.09.023

Podaci o odgovornosti

Gusić, Ivica ; Tadić, Petra

engleski

Injectivity of the specialization homomorphism of elliptic curves

Let E:y^2=x^3+Ax^2+Bx+C be a nonconstant elliptic curve over ℚ(t) with at least one nontrivial ℚ(t)-rational 2-torsion point. We describe a method for finding t0∈ℚ for which the corresponding specialization homomorphism t↦t0∈ℚ is injective. The method can be directly extended to elliptic curves over K(t) for a number field K of class number 1, and in principal for arbitrary number field K. One can use this method to calculate the rank of elliptic curves over ℚ(t) of the form as above, and to prove that given points are free generators. In this paper we illustrate it on some elliptic curves over ℚ(t) from an article by Mestre.

elliptic curve; specialization homomorphism; number field; class number; quadratic field; cubic field; rank; Pari; Magma

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Podaci o izdanju

148

2015.

137-152

objavljeno

0022-314X

10.1016/j.jnt.2014.09.023

Povezanost rada

Matematika

Poveznice
Indeksiranost