The effect of an imposed magnetic field on the flow of an electrically conducting fluid in a channel geometry is investigated numerically using high-performance temporal simulations. For the strongest spanwise magnetic fields considered, the turbulent state appears metastable, which makes the determination of the associated tipping point arduous. As an alternative, edge states, i.e., unstable states located on the state space boundary between the laminar and the turbulent basin of attraction, are investigated in detail. Their continuation smoothly leads to the tipping point where they are expected to collide with the turbulent dynamics. As the magnetic field intensity is raised, edge states become, on average, more energetic and more unstable, while their fluctuations become more chaotic, less predictable, and less symmetric. Nevertheless, their continuation allows one to accurately determine the value of the tipping point beyond which the laminar state becomes the only attractor. Published by the American Physical Society 2024