Hashing into a supersingular elliptic curve
Elligator works just fine for any (including supersingular) elliptic curve with a point of order $2$, with the sole exception of $j=1728$. The latter special case can also be done; see Section 4.2 here.

(The requirement that the curve has a point of order $2$ is trivially fulfilled for supersingular $E/\mathbb F_p$ where $p&gt;3$ is prime, since this implies $\#E(\mathbb F_p)=p+1$ which is always even.)