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You can use the rational_points method:

sage: p1.rational_points()
[(1 : 0 : 1)]
sage: p2.rational_points()
[(-1 : 0 : 1)]

You can use the rational_points method:

sage: p1.rational_points()
[(1 : 0 : 1)]
sage: p2.rational_points()
[(-1 : 0 : 1)]

By the way, also for points defined over other fields:

sage: A.<x,y> = ProjectiveSpace(QQ,1)
sage: X = A.subscheme(x^2 - 2*y^2)
sage: X.rational_points(F=QQbar)
[(-1.414213562373095? : 1), (1.414213562373095? : 1)]