  We prove an equivariant version of Beilinson's conjecture on non-critical
$L$-values of strongly modular abelian varieties over number fields. As an
application, we prove a weak version of Zagier's conjecture on $L(E,2)$ and
Deninger's conjecture on $L(E,3)$ for non-CM strongly modular
$\mathbf{Q}$-curves.
