[Tex/LaTex] Fraction Brackets size

Question

I wanted to write the following equation but somehow my first bracket before the fraction is shorter, last one is fine. but I have no clue what happened to the first one,

also is it possible to write the stuffs under sup as two separate lines, rather than in one line?

\begin{equation}
\begin{aligned}

\Lambda \left( \phi \right) \coloneqq  \adjustlimits\sup_{x,y \in E, x \neq y} \left({\dfrac{ d \left( \phi \left(x\right) , \phi \left(y\right) \right) } {d \left(x, y \right)} } \right) 

\end{aligned}
\end{equation}

Answer 1

The \adjustlimits macro of mathtools is used for getting vertically aligned limits when two operators taking limits follow one another. In this case it's exactly the reason why \left( doesn't do what it's supposed to.

When in a display, \sup behaves exactly like \lim, so there's no special thing to do.

\documentclass{article}
\usepackage{mathtools}

\begin{document}

\begin{equation}
\Lambda(\phi) \coloneqq  \sup_{\substack{x,y \in E\\ x \neq y}}
  \left( \dfrac{d(\phi(x), \phi(y))}{d(x, y)}\right) 
\end{equation}

\end{document}

Note that \left and \right are necessary only around the fraction (but in this case I'd omit those parentheses altogether).

Also aligned is not necessary.