sage: K = GF(19)
sage: E = EllipticCurve(K, [-1, 4])
sage: E
Elliptic Curve defined by y^2 = x^3 + 18*x + 4 over Finite Field of size 19
sage: E.cardinality()
23
sage: P = E.random_element()
sage: P
(0 : 17 : 1)
sage: E(0)
(0 : 1 : 0)