A lamp with an AC lamp burner may include two electrodes spaced apart from one another, a device configured to apply a voltage with alternating polarity to the electrodes; and a reflector, which has a first partial section, which is in the form of a partial body of a first ellipsoid, which has a first and a second focus, or is in the form of a partial body of a first paraboloid, which has a first focus, the reflector having a second partial section, which is in the form of a partial body of a second ellipsoid, which likewise has a first and a second focus or is in the form of a partial body of a second paraboloid, which has a first focus, the first foci of the two ellipsoids or paraboloids being located at different points.