| Résume | Let $J$ be an abelian variety and $A$ be any sub-abelian variety of$J$, both defined over $\Q$. An element of the Tate-Shafarevich group of$A$ is said to be visible in $J$ if the corresponding torsor is isomorphicover $\Q$ to a subvariety of $J$. This concept was introduced byMazur in the context of optimal modular elliptic curves. We show, basedon calculations, assuming the Birch-Swinnerton-Dyer conjecture, that thereare elements of the Tate-Shafarevich group of certain sub-abelian varieitiesof $J_0(p)$ and $J_1(p)$ that are not visible. |
