# How does Edwards curve used for generating public key look like?

What equation suitable for generation of a public key is used for Edwards curve `Ed25519`?

The problem is the following – info on Edwards Elliptic Curve on Wikipedia page presents an equation `y^2 + x^2 = 1 + d * y^2 * x^2` that doesn't allow us to plot a curve depicted on the first picture.

So, what equation is used for `Ed25519`? This one?

``````y^2 + x^2 = 1 - d * y^2 * x^2
``````

Or this one?

``````y^2 + x^2 = 1 + d * y^2 * x^2
``````

I haven't found any documentation covering this topic.

$ax^2 + y^2 = 1 + dx^2y^2$
• I think IOHK used different `a` and `d` values for Ed25519 equation. As far as we can easily build a Bitcoin curve (`secp256k1`) over definite field using its native equation `y^2 = x^3 + 7`, we'll also be able to build a Cardano curve. Sep 10 at 12:33