  Let $\mathcal{E}$ be an elliptic curve over a field $K$ and $\ell$ a prime.
There exists an elliptic curve $\mathcal{E}^*$ related to $\mathcal{E}$ by
anisogeny (rational map that is also a group homomorphisms) of degree $\ell$ if
and only $\Phi_\ell(X, j(\mathcal{E})) = 0$, where $\Phi_\ell(X, Y)$ is the
traditional modular polynomial. Moreover, the modular polynomial gives the
coefficients of $\mathcal{E}^*$, together with parameters needed to build the
isogeny explicitly. Since the traditional modular polynomial has large
coefficients, many families with smaller coefficients can be used instead, as
described by Elkies, Atkin and others. In this work, we concentrate on the
computation of the family of modular polynomials introduced by Charlap, Coley
and Robbins. It has the advantage of giving directly the coefficients of
$\mathcal{E}^*$ as roots of these polynomials. We review and adapt the known
algorithms to perform the computations of modular polynomials. After describing
the use of series computations, we investigate fast algorithms using floating
point numbers based on fast numerical evaluation of Eisenstein series. We also
explain how to use isogeny volcanoes as an alternative.
