Geometrically simple abelian surfaces over Q with small conductor are shown to have (Z/pZ)^2 in their Tate–Shafarevich groups for p = 5, 7, 11, 13, via modular-form congruences and visibility.
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Modular abelian surfaces of small conductor with nontrivial Tate--Shafarevich groups
Geometrically simple abelian surfaces over Q with small conductor are shown to have (Z/pZ)^2 in their Tate–Shafarevich groups for p = 5, 7, 11, 13, via modular-form congruences and visibility.