  We study genus one curves that arise as 2-, 3- and 4-coverings of elliptic
curves. We describe efficient algorithms for testing local solubility and
modify the classical formulae for the covering maps so that they work in all
characteristics. These ingredients are then combined to give explicit bounds
relating the height of a rational point on one of the covering curves to the
height of its image on the elliptic curve. We use our results to improve the
existing methods for searching for rational points on elliptic curves.
