The group order #E(F_p) is the size of the elliptic-curve group ECM works in for this (parametrization, σ). ECM finds the prime factor p exactly when this order is B1-smooth (all prime factors ≤ B1), or B1-smooth apart from one prime ≤ B2. So the largest prime factor above is the B1 that would reveal p on this curve - the reason a given sigma “worked”. The curve itself is built by GMP-ECM, so the parametrization/σ conventions match ecm -sigma param:sigma exactly.