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Every plane has 3 or more. There is a projective (or affine) plane with only 3 points.
Parallel lines in the Euclidean plane do not intersect but all parallel lines in the projective plane intersect at the point at infinity.
An infinite number in a Euclidean plane - which is the "normmal" plane. Some selected numbers in the finite or affine planes (but you need to be studying projective geometry to come across these).
A minimum of three points are required to define a plne (if they are not collinear). And in projective geometry you can have a plane with only 3 points. Boring, but true. In normal circumstances, a plane will have infinitely many points. Not only that, there are infinitely many in the tiniest portion of the plane.
whet is real and complex plane