Reference multiple equations, same parentheses

I have a list of equations that I want to reference all grouped together in the same pair of parentheses (…). How should I proceed? I am aware of the cleveref package, which does indeed group equations together, but (as far as I can tell) not within the same parentheses.

Minimum working example:

documentclass{article}
usepackage{amsmath}
usepackage{cleveref}
usepackage[parfill]{parskip}

begin{document}
First equation:
begin{equation}
    label{1}
    E=mc^2
end{equation}
Second equation:
begin{equation}
    label{2}
    e^{i pi}+1=0
end{equation}
Third equation:
begin{equation}
    label{3}
    a^n+b^n=c^n
end{equation}
Reference with texttt{eqref}: Eqs. eqref{1}, eqref{2}, eqref{3}

Reference with texttt{cleveref}: cref{1,2,3} 

Again with texttt{cleveref}: labelcref{1,2,3} 

What I actually want: Eqs. (1,2,3)
end{document}

documentclass{article}
usepackage{cleveref}
crefname{equation}{Eq}{Eqs} % capitalize "E", no period
crefrangelabelformat{equation}{(#3#1#4--#5#2#6)}
begin{document}
cref{eq1,eq2,eq3,eq4,eq5}. crefrange{eq1}{eq5}.

% Five equation-related label directives:
refstepcounter{equation} label{eq1}
refstepcounter{equation} label{eq2}
refstepcounter{equation} label{eq3}
refstepcounter{equation} label{eq4}
refstepcounter{equation} label{eq5}
end{document}