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I have the following code where I can't really figure out how to rotate the table 180 degrees:

\documentclass{article}
\usepackage[utf8]{inputenc}
\usepackage{graphicx}
\graphicspath{{images/}}
\usepackage{setspace}
\usepackage{mathrsfs}
\usepackage{amsmath}
\usepackage{cellspace}
\setlength\cellspacetoplimit{4pt}
\setlength\cellspacebottomlimit{4pt}
\usepackage{tabularx,ragged2e,booktabs,caption}
\usepackage{rotating}
\newcolumntype{C}{>{\Centering\arraybackslash}X}
\newcommand\swb{{\scriptstyle\Box}} % "small white box"
\usepackage{mathtools}
\usepackage{amssymb,bm}


\begin{document}
\begin{sidewaystable}
\captionof{table}{Points on $E$ given by $nP + \varepsilon T$ with $\varepsilon = 0$} \label{table:2}
\scriptsize
\begin{tabular}{| *{4}{Sc|}}
  \hline
  $n$ & $nP=(x_n,y_n)$ & $Z(nP)$ & $\boxtimes$ / $\Box$ \\ \hline
  $\vdots$ & $\vdots$ & $\vdots$ & $\boxtimes$ \\ \hline
  $-10$ & $\bigg(\dfrac{56424579}{207025}, \dfrac{414903626892}{94196375}\bigg)$ & $2^{24} \cdot 3^{36} \cdot 5^{-32} \cdot 7^{-32} \cdot 13^{-32} \cdot 19^2 \cdot 29 \cdot 41 \cdot 83^2 \cdot 137^4 \cdot 661 \cdot 2677 \cdot 107581 \cdot 165713^{12} \cdot 631292953$ & $\boxtimes$ \\ \hline
  $-9$ & $\bigg(\dfrac{-1094394}{18769}, \dfrac{500465142}{2571353}\bigg)$ & $2^{36} \cdot 3^{48} \cdot 11^{12} \cdot 13 \cdot 19^4 \cdot 37^2 \cdot 127^{12} \cdot 137^{-32} \cdot 9377 \cdot 96181 \cdot 1997236169$ & $\boxtimes$ \\ \hline
\end{tabular}
\end{sidewaystable}
\end{document}
1

As far as I understand, you want the opposite position of tables with captions. It is given by an option of style (marked %here PS in the example):

\documentclass{article}
\usepackage[utf8]{inputenc}
\usepackage{graphicx}
\graphicspath{{images/}}
\usepackage{setspace}
\usepackage{mathrsfs}
\usepackage{amsmath}
\usepackage{cellspace}
\setlength\cellspacetoplimit{4pt}
\setlength\cellspacebottomlimit{4pt}
\usepackage{tabularx,ragged2e,booktabs,caption}
\usepackage[figuresleft]{rotating} %here PS
\newcolumntype{C}{>{\Centering\arraybackslash}X}
\newcommand\swb{{\scriptstyle\Box}} % "small white box"
\usepackage{mathtools}
\usepackage{amssymb,bm}


\begin{document}
\begin{sidewaystable}
\captionof{table}{Points on $E$ given by $nP + \varepsilon T$ with $\varepsilon = 0$} \label{table:2}
\scriptsize
\begin{tabular}{| *{4}{Sc|}}
  \hline
  $n$ & $nP=(x_n,y_n)$ & $Z(nP)$ & $\boxtimes$ / $\Box$ \\ \hline
  $\vdots$ & $\vdots$ & $\vdots$ & $\boxtimes$ \\ \hline
  $-10$ & $\bigg(\dfrac{56424579}{207025}, \dfrac{414903626892}{94196375}\bigg)$ & $2^{24} \cdot 3^{36} \cdot 5^{-32} \cdot 7^{-32} \cdot 13^{-32} \cdot 19^2 \cdot 29 \cdot 41 \cdot 83^2 \cdot 137^4 \cdot 661 \cdot 2677 \cdot 107581 \cdot 165713^{12} \cdot 631292953$ & $\boxtimes$ \\ \hline
  $-9$ & $\bigg(\dfrac{-1094394}{18769}, \dfrac{500465142}{2571353}\bigg)$ & $2^{36} \cdot 3^{48} \cdot 11^{12} \cdot 13 \cdot 19^4 \cdot 37^2 \cdot 127^{12} \cdot 137^{-32} \cdot 9377 \cdot 96181 \cdot 1997236169$ & $\boxtimes$ \\ \hline
\end{tabular}
\end{sidewaystable}
\end{document}

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