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Non-trivial Shafarevich-Tate Groups of Elliptic Curves (1703.05909v1)

Published 17 Mar 2017 in math.NT

Abstract: We characterize quadratic twists of $y^{2=x(x-a^{2)(x+b^2)$}} with Mordell-Weil groups and $2$-primary part of Shafarevich-Tate groups being isomorphic to $(\mathb Z/2\mathbb Z)^2$ under certain conditions. We also obtain the distribution result of these elliptic curves.