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arXiv · 1003.4393

On quadratic twists of elliptic curves and some applications of a refined version of Yu's formula

Derong Qiu
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Abstract

In this paper, we study some cohomology groups and quadratic twists of elliptic curves, and apply Tate local duality and the results of Kramer-Tunnell on local norm cokernel to give a refined version of Yu's formula in the case of elliptic curves. Then, by using this refinement formula, we obtain explicit orders of Shafarevich-Tate groups of some elliptic curves in quadratic number fields, including a few unconditional cases.

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Derong Qiu. 2014-06-30. On quadratic twists of elliptic curves and some applications of a refined version of Yu's formula. https://doi.org/10.1080/00927872.2013.830731

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