> J := J0(65); J;
Modular abelian variety J0(65) of dimension 5 and level 5*13 over Q
> D := Decomposition(J); D;
> [
    Modular abelian variety 65A of dimension 1, level 5*13 and
    conductor 5*13 over Q,
    Modular abelian variety 65B of dimension 2, level 5*13 and
    conductor 5^2*13^2 over Q,
    Modular abelian variety 65C of dimension 2, level 5*13 and
    conductor 5^2*13^2 over Q
]
> #(D[1] meet D[2]);
2
> IsIsomorphic(D[2],Dual(D[2]));
true Homomorphism from 65B to modular abelian variety of
dimension 2 given on integral homology by:
[ 1  0  0 -1]
[ 0  1  0 -1]
[ 0  0  1 -1]
[ 0 -1  1 -1]
> L := LSeries(D[2]);
> LRatio(L,1);
1/6