  We obtain an upper bound on the lowest magnetic Neumann eigenvalue of a
bounded, convex, smooth, planar domain with moderate intensity of the
homogeneous magnetic field. This bound is given as a product of a purely
geometric factor expressed in terms of the torsion function and of the lowest
magnetic Neumann eigenvalue of the disk having the same maximal value of the
torsion function as the domain. The bound is sharp in the sense that equality
is attained for disks. Furthermore, we derive from our upper bound that the
lowest magnetic Neumann eigenvalue with the homogeneous magnetic field is
maximized by the disk among all ellipses of fixed area provided that the
intensity of the magnetic field does not exceed an explicit constant dependent
only on the fixed area.
