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In [[number theory]], the '''classical modular curve''' is an irreducible [[algebraic curve|plane algebraic curve]] given by an equation
:Φ<sub>n</sub>(x, y)=0, where for the [[j-invariant]] j(τ), :x=j(n τ), y=j(τ) 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). == Geometry of the modular curve ==
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