most citedOn the density of abelian surfaces with Tate- Shafarevich group of order five times a square

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math.NT2013★ 1 cited

On the density of abelian surfaces with Tate- Shafarevich group of order five times a square

Stefan Keil, Remke Kloosterman

Let A=E_1xE_2 be be the product of two elliptic curves over QQ, both having a rational five torsion point P_i. Set B=A/<(P_1,P_2)>. In this paper we give an algorithm to decide whe…

math.NT2012

Examples of non-simple abelian surfaces over the rationals with non-square order Tate-Shafarevich group

Stefan Keil

Let A be an abelian surface over a fixed number field. If A is principally polarised, then it is known that the order of the Tate-Shafarevich group of A must, if finite, be a squar…