A local magnetic equilibrium model is presented, with finite inverse aspect ratio and up-down asymmetrically shaped cross section, that depends on eight free parameters. In contrast with other local equilibria, which provide simple magnetic-surface parametrisations at the cost of complex poloidal-field flux descriptions, the proposed model is intentionally built to afford analytically tractable magnetic-field components. Therefore, it is particularly suitable for analytical assessments of equilibrium-shaping effects on a variety of tokamak-plasma phenomena.