  The SEA algorithm for computing the cardinality of elliptic curves over
finite fields in many characteristic uses modular polynomials. These
polynomials come into different flavors, and methods to compute them
flourished. 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 formulas
involve derivatives of the modular polynomial that may sometime vanish. One way
to overcome this problem is to use alternative trivariate polynomials $U_\ell$,
$V_\ell$, and $W_\ell$ introduced by Charlap, Coley and Robbins to overcome
some difficulties in the first versions of Elkies's approach. We give
properties of these polynomials, as well as formulas to compute the isogenous
curve that were sketched by Atkin. Also we investigate another suggestion of
Atkin using modular polynomials associated to a power product of Dedekind's
$\eta$ function.
