Hi Matadem, here attached is the set up for your shape using rail revolve.

First select the profile curve:



Run Construct > Revolve > Rail revolve.

The prompt will say "Select rail curve". Select the top ellipse edge:



The next prompts will say "Pick revolve axis start point" and then "Pick revolve axis end point". Pick these 2 points on the center axis line:



A solid dome with the bottom capped will be created and you can boolean union this onto the base extrusion.

- Michael