Let Z be Zermelo's system without choice (C) and without axiom of foundation (AF), namely extensionnality, pair, union, power set, separation, empty set, infinity. My question is the following one :

Is Z equiconsistent with Z+C ?

[I would also be interested it knowing whether Z+AF is equiconsistent with Z+AF+C, but I guess this is fairly close, and not as important to me]

I know that ZF is equiconsistent with ZF+C, so this is really a question without the replacement axiom.

I asked several specialists in set theory and they could not help me on this.

Any idea/reference on this question ?