I use Sagemath's built-in function
discrete_log() to solve ECDLP and according to the documentation it uses Pohling-Hellman algorithm to solve an ECDLP.
This is the case for my EC:
P-order => 176648753626148987385153422443570230330 Q-order() => 2
The P-order has these prime factors: 2 * 3 * 5 * 5888291787538299579505114081452341011
Even though the highest prime factor is super-large, the ECDLP through
discrete_log() is solved within a second.
I Read about the Pohling-hellman attack and it only mentions that P should have small prime-factors in order for the attack to be successful. It never mentions the order of Q.
How does the order of Q affect the time it takes for the attack to be successful?