Four 3D points neither colinear nor coplanar on the surface of a minimal volume ellipsoid

${\color{#D61F06}\text{This problem's question:}}$ What is the $\frac{\text{volume of ellipsoid}}{\text{volume of tetrahedron}}?$

Given four three-dimensional points, such that no three points are colinear and all four points are not coplanar on the surface of a minimal volume ellipsoid, what is the $\frac{\text{volume of ellipsoid}}{\text{volume of tetrahedron}}?$

The four three-dimensional points' coordinates are not supplied as they are not necessary to solve this problem. Bonus: why is this true?