Modular abelian varieties

My primary objective is to verify the BSD conjecture for specific modular abelian varieties by using the rich theory of their arithmetic.

The BSD conjecture asserts that if A is a modular abelian variety with $L(A,1)\neq 0$, then

$$\frac{L(A,1)}{\Omega_A} = \frac{\char93 \mbox{\cyr X}(A)\cdot... ... A(\mathbf{Q})_{\tor}\cdot\char93 A^{\vee}(\mathbf{Q})_{\tor}}.$$

Here $A(\mathbf{Q})_{\tor}$ is the group of rational torsion points on A; the Shafarevich-Tate group $\mbox{\cyr X}(A)$ is a measure of the failure of the local-to-global principle; the Tamagawa numbers c_p are the orders of certain component groups associated to A; the real number $\Omega_A$ is the volume of  A(R) with respect to a basis of differentials having everywhere nonzero good reduction; and $A^{\vee}$ is the dual of A.