Your question is a good example of how difficult it can be to figure out.
Many teachers would correct your sentence in this way:
<How do you figure out if there is an ellipsis? >
But, if you had intended to ellipt ""or not", from the end of your question, it could be:
How do you figure out whether there is an ellipsis?
Because "whether" and "or" normally go together:
How do you figure out whether there is an ellipsis (or not)?
You should read up on ellipsis.