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is a point on the curve. The curve is sometimes called X<sub>0</sub>(n), though often that is used for the abstract [[algebraic curve]] for which there exist various models. A related object is the '''classical modular polynomial''', a polynomial in one variable defined as Φ<sub>n</sub>(x, x).
It is important to note that the classical modular curves are part of the larger theory of [[modular curve|modular curves]]. In particular it has another expression as a compactified quotient of the complex [[upper half-plane]] ''H''.
== Geometry of the modular curve ==
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