The curve has j-invariant 0, and so has an automorphism group of size 6. Hence, it is possible to perform the Pollard rho algorithm using equivalence classes of size 6.

They used n = 1024 partitions for the random walk, and the “hash function” \eta was chosen to be the least significant \log_2(n) bits of the x-coordinate of the current curve point.

The paper writes that “The parallel implementation of the rho method by adopting a client-server model, using 2000 CPU cores took about 6 months”. They seem to have been lucky to get a collision earlier than expected: “the result of the authors attack is little bit better than the average number of rational points where a simple collision attack stops.”