How is it possible that mathematica can’t calculate the eigenvectors and eigenvalues of this?

How is it possible that mathematica can’t calculate the eigenvectors and eigenvalues of this:

Code:

$  Assumptions = f \[Element] Reals ; \[CapitalNu] = (1/(4*Cosh[f]^3))*{{Exp[f]*(Cosh[f])^2, Exp[f],      Cosh[f], Cosh[f]}, {Exp[f], Exp[f]*(Cosh[f])^2, Cosh[f],      Cosh[f]}, {Cosh[f], Cosh[f], Exp[-f]*(Cosh[f])^2,      Exp[-f]}, {Cosh[f], Cosh[f], Exp[-f], Exp[-f]*(Cosh[f])^2}} Eigensystem[N]  

Image:

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It is not very hard on paper(I ‘ve done it) but it has too many calculations. I ‘ve seen mathematica doing way harder things but it just failed on this one…

Where is my mistake?