Neighborhood of the supersingular elliptic curve isogeny graph at j = 0 and 1728

Abstract We describe the neighborhood of the vertex [ E 0 ] (resp. [ E 1728 ] ) in the l-isogeny graph G l ( F p 2 , − 2 p ) of supersingular elliptic curves over the finite field F p 2 when p > 3 l 2 (resp. p > 4 l 2 ) with E 0 : y 2 = x 3 + 1 (resp. E 1728 : y 2 = x 3 + x ) supersingular.