Building on Finotti in (Acta Arith 139(3):265–273, 2009), we give an elementary proof for the well known result that there exactly $$\lceil (p-1)/4 \rceil -\lfloor (p-1)/6 \rfloor$$ supersingular elliptic curves in characteristic p. We use a related polynomial instead of the supersingular polynomial itself to simplify the proof and this idea might be helpful to prove other results related to the supersingular polynomial.