The equilibrium conformations of a flexible permanent magnetic filament that consists of a sequence of linked magnetic colloidal nanoparticles with short-ranged Lennard-Jones attractive interactions (Stockmayer polymer) are thoroughly analysed via Langevin dynamics simulations. A tentative phasediagram is presented for a chain of length N 1⁄4 100. The phase diagram exhibits several unusualconformational phases when compared to non-magnetic chains. These phases are characterised by a large degree of conformational anisotropy, and consist of closed chains, helicoidal-like states, partially collapsed states, and very compact disordered states. The phase diagram contains several interesting features like the existence of at least two ‘triple points’.