Score:1

Are (0,0) the coordinates of the "point at infinity"?

nz flag

Christel Bach's elliptic curve calculator has the coordinates for the "point at infinity" be $(0,0)$. Is that just a stand-in?

Score:1
my flag

Is that just a stand-in?

Yes, it is. The "point at infinity" doesn't actually correspond to a solution to the underlying equation, but instead is an artificial point we add to make the group operation complete.

That said, if we need to express that point in a software package, we need to have some encoding of it - assuming that $x=y=0$ isn't a solution to the equation (e.g. if the equation is $y^2 = x^3 + ax + b$, then $b \ne 0$), it's as good as any...

I sit in a Tesla and translated this thread with Ai:

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