Let N = p q N=pq be a product of two distinct primes. There is an isogeny J 0 ( N ) n e w → J N J_0(N)^\mathrm {new}\to J^N defined over Q \mathbf {Q} between the new quotient J 0 ( N ) J_0(N) and the Jacobian of the Shimura curve attached to indefinite quaternion algebra of discriminant N N . In the case when p = 2 , 3 , 5 , 7 , 13 p=2,3,5,7,13 , Ogg made predictions about the kernels of these isogenies. We show that Ogg’s conjecture is false in general. Afterwards, we propose a strategy for proving results toward Ogg’s conjecture in certain situations. Finally, we discuss this strategy in detail for N = 5 ⋅ 13 N=5\cdot 13 .