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such that {{math|(''x'', ''y'') {{=}} (''j''(''nτ''), ''j''(''τ''))}} is a point on the curve. Here {{math|''j''(''τ'')}} denotes the [[j-invariant|{{mvar|j}}-invariant]].
The curve is sometimes called {{math|''X''<sub>0</sub>(''n'')}}, though often that notation 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 {{math|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]]s. In particular it has another expression as a compactified quotient of the complex [[upper half-plane]] {{math|'''H'''}}.
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