  The classical modular equations involve bivariate polynomials that can be
seen to be univariate with coefficients in the modular invariant $j$. Kiepert
found modular equations relating some $\eta$-quotients and the Weber functions
$\gamma_2$ and $\gamma_3$. In the present work, we extend this idea to double
$\eta$-quotients and characterize all the parameters leading to this kind of
equation. We give some properties of these equations, explain how to compute
them and give numerical examples.

Number Theory