The socalled classinvariant homomorphism $\psi_n$, introduced by M.
J. Taylor, measures the Galois module structure of (rings of integers
of) extensions of the form $K(\frac{1}{n}P)/K$, where $K$ is a number
field, $P$ is a $K$rational point on an abelian variety $A$, and
$n>1$ is an integer. When $A$ is an elliptic curve and $n$ is coprime
to 6, then $\psi_n$ vanishes on torsion points. We explain here how,
using Weil restrictions of elliptic curves, it is possible to
construct abelian varieties of higher dimension for which this
vanishing result is no longer true.
