[Tex/LaTex] Increase the height of the row in the table

tables

I have the following code:

\usepackage{tabularx,array}
\usepackage{tabu}
\begin{tabular}{| c | c | c | c | }
    \hline
    $n$ & $nP_\star=(x_n,y_n)$ & $z(nP_\star)$  & $\boxtimes$ / $\Box$ \\ \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
$-8$ & $\bigg(\dfrac{32971}{361}, \dfrac{-4894012}{6859}\bigg)$ & $2^{28} \cdot 3^6 \cdot 11^2 \cdot 19^{-32} \cdot 37^4 \cdot 61^{12} \cdot 101^{12} \cdot 397 \cdot 1061 \cdot 21937$ & $\boxtimes$ \\ \hline
$-7$ & $\bigg(\dfrac{20499}{1369}, \dfrac{418284}{50653}\bigg)$ & $2^{32} \cdot 3^{44} \cdot 5^{14} \cdot 7^{14} \cdot 13^{12} \cdot 37^{-32} \cdot 41 \cdot 433 \cdot 101873$ & $\boxtimes$ \\ \hline
 \end{tabular}

I have two problems here.

  1. I need to increase the row height as my second column consists of fraction coordinates and the space looks so tight. I tried using \vspace unfortunately it leaves quite a gap which does not look proper.

  2. My table consist of 4 column. Some how since the data on the third column is too long, it get cuts off. I tried using \\ at the end of the data but it seems to be sending the behind part of the data to a different column. Is there a way of making it look better?

A picture is attached as well.enter image description here

Best Answer

I suggest you insert (typographic) struts in the numerator and denominator terms; one strut each per row suffices.

enter image description here

\documentclass{article}

%% Define a few struts
%% (from code by Claudio Beccari in TeX and TUG News, Vol. 2, 1993)
\newcommand\Tstrut{\rule{0pt}{2.9ex}}       % "top" strut
\newcommand\Bstrut{\rule[-1.3ex]{0pt}{0pt}} % "bottom" strut
\newcommand\TBstrut{\Tstrut\Bstrut}         % "top and bottom" strut

\usepackage{amsmath,amssymb}
\usepackage[a4paper,margin=1in]{geometry} % set page parameters
\usepackage{rotating} % for "sideways" environment

\begin{document}
\begin{sideways} % switch to landscape mode
\noindent
$\begin{array}{| c | c | c | c | }
    \hline
    n\TBstrut & nP_\star=(x_n,y_n) & z(nP_\star)  & \boxtimes / \Box \\ \hline
    \vdots & \vdots & \vdots & \boxtimes \\ \hline
-10 & \biggl(\dfrac{\Tstrut56424579}{\Bstrut207025}, \dfrac{414903626892}{94196375}\biggr) & 2^{24} \cdot 3^{36} \cdot 5^{-32} \cdot 7^{-32} \cdot 13^{-32} \cdot  19^2 \cdot 29 \cdot 41 \cdot 83^2 \cdot 137^4 \cdot 661 \cdot 2677 \cdot 107581 \cdot 165713^{12} \cdot 631292953 & \boxtimes \\ \hline
-9 & \biggl(\dfrac{\Tstrut{-1094394}}{\Bstrut18769}, \dfrac{500465142}{2571353}\biggr) & 2^{36} \cdot 3^{48} \cdot 11^{12} \cdot 13 \cdot 19^4 \cdot 37^2 \cdot 127^{12} \cdot 137^{-32} \cdot 9377 \cdot 96181 \cdot 1997236169 & \boxtimes \\ \hline
-8 & \biggl(\dfrac{\Tstrut32971}{\Bstrut361}, \dfrac{-4894012}{6859}\biggr) & 2^{28} \cdot 3^6 \cdot 11^2 \cdot 19^{-32} \cdot 37^4 \cdot 61^{12} \cdot 101^{12} \cdot 397 \cdot 1061 \cdot 21937 & \boxtimes \\ \hline
-7 & \biggl(\dfrac{\Tstrut20499}{\Bstrut1369}, \dfrac{418284}{50653}\biggr) & 2^{32} \cdot 3^{44} \cdot 5^{14} \cdot 7^{14} \cdot 13^{12} \cdot 37^{-32} \cdot 41 \cdot 433 \cdot 101873 & \boxtimes \\ \hline
 \end{array}$
\end{sideways}
\end{document}
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