Data for "Behaviour of the order of Tate-Shafarevich groups for the quadratic twists of elliptic curves"

This dataset contains data for the article: Andrzej Dąbrowski, Lucjan Szymaszkiewicz, Behavior of the order of Tate-Shafarevich groups for the quadratic twists of elliptic curves.

Description of the files:A.txt - data for the curve y^2 = x^3-x (denoted by A in the article)B.txt - data for the curve y^2 = x^3-1 (denoted by B in the article)C.txt - data for the curve y^2 = x^3+4*x^2-16 (denoted by C in the article)D.txt - data for the curve y^2 = x^3-x^2-8*x-16 (denoted by D in the article)

Each file contains three columns (separated by tabs).

In the first column we find the value d by which we twist the given curve. In the second column the value of the coefficient a(d). In the third the value sqrt(|Sha(E_d)|) if a(d) != 0, otherwise 0.

The files contain all considered d values for d less than a billion.