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A criterion for injectivity of the specialization homomorphism of elliptic curves and its applications (CROSBI ID 633651)

Prilog sa skupa u zborniku | sažetak izlaganja sa skupa

Tadić, Petra A criterion for injectivity of the specialization homomorphism of elliptic curves and its applications // Computational Aspects of Diophantine Equations. 2016. str. 26-26

Podaci o odgovornosti

Tadić, Petra

engleski

A criterion for injectivity of the specialization homomorphism of elliptic curves and its applications

Let $K$ be a number field. Let $E$ be a nonconstant elliptic curve over $K(t)$ with at least one nontrivial $K(t)$-rational $2$- torsion point. By the Silverman specialization theorem the specialization homomorphism $t\mapsto t_0$ is injective for all but finitely many $t_0\in K$. For $K$ of class number one, Gusi\' c and Tadi\' c obtained a method for finding $t_0\in K$ for which the corresponding specialization homomorphism is injective. In principal they extended the method to arbitrary number fields $K$. This method can be used to calculate the rank of elliptic curves of the form as above, by looking at the structure of a chosen specialized curve. This method has been used by Gusi\' c, Dujella, Peral and Tadi\' c to calculate exactly the rank of some record high rank elliptic curves over $\mathbb Q(t).$

elliptic curves ; rank ; function fields ; generators ; injectivity ; specialization homomorphism

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Podaci o prilogu

26-26.

2016.

objavljeno

Podaci o matičnoj publikaciji

Computational Aspects of Diophantine Equations

Podaci o skupu

Computational Aspects of Diophantine Equations

predavanje

15.02.2016-19.02.2016

Salzburg, Austrija

Povezanost rada

Matematika