@forest That depends on how you want to interpret "the private key". In ECC you have "the curve", which has parameters (p, a, b, G, n, h). The private key d is any integer in [1, n), and the public key is d*G=Q, transmitted as the X coordinate of Q and either the Y coordinate or a way of knowing which of the two is the right answer. So the private key is either d or (d, the curve), depending on how you want to look at it.