Injectivity of the specialization homomorphism of elliptic curves (CROSBI ID 622618)
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Podaci o odgovornosti
Tadić, Petra
engleski
Injectivity of the specialization homomorphism of elliptic curves
Let E be a nonconstant elliptic curve over Q(t) with at least one nontrivial Q(t)-rational 2-torsion point. By the Silverman specialization theorem the specialization homomorphism t --> t0 is injective for all but finitely many t0 ∈ Q. We describe a method for finding t0 ∈ Q for which the corresponding specialization homomorphism 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. This is an improvement of a result from one of our former preprints on this topic. We show how this method can be used to calculate the rank of elliptic curves over Q(t) of the form as above, by observing a chosen specialized curve. This is a joint work with I. Gusic.
elliptic curve; specialization homomorphism
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Podaci o prilogu
13-13.
2014.
objavljeno
Podaci o matičnoj publikaciji
Workshop on Number Theory and Algebra
Podaci o skupu
Workshop on Number Theory and Algebra on the occasion of 60th birthday of Ivica Gusić
pozvano predavanje
26.11.2014-28.11.2014
Zagreb, Hrvatska