How to sketch a function

Question

I want to scketch the following function

$$\varphi_s(q,p)=\frac{1}{\sqrt{\pi}}e^{\Large{-\frac{\Big(\cosh(s)q(s)+\sinh(s)p(s)\Big)^2+\Big(\sinh(s)q(s)+\cosh(s)p(s)\Big)^2}{2}}}$$ with $s\ge 0$

where the two axes are $q(t)$ and $p(t)$ for all $t\ge 0$

Thanks for your help