As a continuation of a previous study, the magnetic configuration of the torsatron with ℓ = 2 helical windings and no toroidal field coils is investigated. A useful volume with closed toroidal magnetic surfaces exists only for sufficiently large pitch angles of the helical windings (> 45°). With increasing pitch angle the rotational transform on the magnetic axis decreases, and high shear is obtained (Θ ∼ 1). In this case, the mirror ratio along the field lines is relatively high (Bmax/Bmin > 1.5). If we require low mirror ratio (Bmax/Bmin < 1.5) the ℓ = 2 configuration is limited to low shear, in contrast to the previously studied case ℓ = 3 which has considerable shear even when the mirror ratio is low.