Confusion regarding dependencies

Question

Let say we have a relation with 5 attributes {A, B, C, D, E}. Let say we have two candidate keys as A and B,C. Let us say we have a partial dependency as B -> E with regards to the candidate key B,C. The database designer decides that A will be the primary key of the relation. Now since we had B -> E, will it be called a partial dependency or a transitive dependency? Is the relation 2NF or not even 2NF?