How Is the Specific Base Point for a Curve like Secp256k1 Chosen?

The base point (G) for a standardized curve like secp256k1 is not chosen arbitrarily but is part of the publicly defined parameters for that curve. It is selected to be a point on the curve that generates a subgroup of a very large prime order (n).

The specific coordinates of G are derived from a set of deterministic, verifiable procedures to ensure there are no backdoors or weaknesses. The choice is made to maximize the difficulty of solving the elliptic curve discrete logarithm problem.