For a finite field elliptic curve we can search for the first 10 points for a curve of \(y^2 = x^3 + ax +b\) and for a defined prime number (\(p\)). In this case we use a number of standard curves including Curve25519 (as used in Tor), secp256k1 (as used in Bitcoin) and NIST P-256. In this case we use the Legendre symbol to determine if there is a valid square root for \(y\). With P-256 we use:
\(p = 2^{256} - 2^{224} + 2^{192} + 2^{96} - 1 \), \(a= -3\), \(b=41058363725152142129326129780047268409114441015993725554835256314039467401291\)