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Let $X\subset Y(1)^n$ be a subvariety defined over a number field $\mathbb F$and let $(P_1,\ldots,P_n)\in X$ be a special point not contained in apositive-dimensional special subvariety of $X$. We show that the if acoordinate $P_i$ corresponds to an order not contained in a single exceptionalSiegel-Tatuzawa imaginary quadratic field $K_*$ then the associateddiscriminant $|\Delta(P_i)|$ is bounded by an effective constant depending onlyon $\operatorname{deg} X$ and $[{\mathbb F}:{\mathbb Q}]$. We derive analogouseffective results for the positive-dimensional maximal special subvarieties.  From the main theorem we deduce various effective results of Andr\'e-Oorttype. In particular we define a genericity condition on the leading homogeneouspart of a polynomial, and give a fully effective Andr\'e-Oort statement forhypersurfaces defined by polynomials satisfying this condition.

Some effective estimates for Andr\'e-Oort in $Y(1)^n$