We study the problem of generating the endomorphism ring of a supersingular elliptic curve by two cycles in ℓ-isogeny graphs. We prove a necessary and sufficient condition for the two endomorphisms corresponding to two cycles to be linearly independent, expanding on the work by Kohel in his thesis. We also give a criterion under which the ring generated by two cycles is not a maximal order. We give some examples in which we compute cycles which generate the full endomorphism ring. The most difficult part of these computations is the calculation of the trace of these cycles. We show that a generalization of Schoof’s algorithm can accomplish this computation efficiently.