p-values for a magnification factor equal to or larger than ten for each of the simulated lenses. The left panel shows the p-values for the lightest halo mass (3 × 10¹¹ M_⊙) for all axion masses. Middle and right panels show the equivalent p-values for the 7 × 10¹¹ M_⊙ and 4 × 10¹² M_⊙ haloes, respectively. The grey lines represent the complementary p-values for the CDM model at each halo mass. Halo masses increase from left to right with green, blue, and purple colours. The squares, circles, and triangles represent different axion masses, increasing in this order. Dashed, horizontal lines indicate the significance of finding an image with magnification equal to or greater than ten for each model. For the smooth model, it is virtually impossible to achieve such magnification at a distance to the centre of the halo equal to half that of the CC.