Elliptic Nodes

a and b is not given, but since we are given the two points, generator G and the public key point P, we can construct two equations in the form of $y ^ 2 = x ^ 3 + ax + b$. Solving the two linear congruent equation should give us $a, b$. Trying to do E = EllipticCurve(GF(p), [a, b]) lead to an error by Sage that the curve defined is not a elliptic curve, rather a singular curve....