In this paper, we approach the study of modules of constant Jordan type and equal images modules over elementary abelian p-groups Er of rank r⩾2 by exploiting a functor from the module category of a generalized Beilinson algebra B(n, r), n⩽p, to mod Er. We define analogues of the above-mentioned properties in mod B(n, r) and give a homological characterization of the resulting subcategories via a ℙr−1-family of B(n, r)-modules of projective dimension 1. This enables us to apply general methods from Auslander–Reiten theory and thereby arrive at results that, in particular, contrast the findings for equal images modules of Loewy length 2 over E2 by Carlson, Friedlander and Suslin [Commentarii Math. Helv. 86 (2011) 609–657] with the case r>2. Moreover, we give a generalization of the W-modules introduced by the aforementioned authors.