How can I transform a complete twisted Edwards curve $ax^2+y^2 = 1+dx^2y^2$ with not square $d$ and square $a$ into an isomorphic Edwards curve $X^2+Y^2 = 1+DX^2Y^2$ with a square $-D$ i.e. $D = -r^2$?
I tried to set $X = \frac{x}{\sqrt{a}}; Y=y$, but $-\frac{d}{a}$ is also a non square (at least for Edwards25519). This answer is not working as well (i.e. $-1/d$ is not a square), because $-1$ is square.
Is it even possible to do such a transformation?
