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The SEA algorithm for computing the cardinality of elliptic curves overfinite fields in many characteristic uses modular polynomials. Thesepolynomials come into different flavors, and methods to compute themflourished. Once equipped with some modular polynomials for prime $\ell$,algebraic formulas are used to compute a curve $\mathcal{E}^*/\mathbb{F}_q$that is $\ell$-isogenous to the curve of interest $\mathcal{E}$. These formulasinvolve derivatives of the modular polynomial that may sometime vanish. One wayto overcome this problem is to use alternative trivariate polynomials $U_\ell$,$V_\ell$, and $W_\ell$ introduced by Charlap, Coley and Robbins to overcomesome difficulties in the first versions of Elkies's approach. We giveproperties of these polynomials, as well as formulas to compute the isogenouscurve that were sketched by Atkin. Also we investigate another suggestion ofAtkin using modular polynomials associated to a power product of Dedekind's$\eta$ function.

Using the Charlap-Coley-Robbins polynomials for computing isogenies