J0389 := CuspidalSubspace(ModularSymbols(389));
A     := NewformDecomposition(J0389 : Proof := false)[5];
A;

L1overOmega := LRatio(A,1);
"L1/Omega = ", L1overOmega;

T     := TorsionBound(A,7);
"Torsion  = ", T;

c389  := TamagawaNumber(A,389);
"Tamagawa number = ", c389;

ShaConj := L1overOmega*T^2/c389;

"Conjectural order of Sha = ", Factorization(Integers()!ShaConj);