Is this sentence a fragment Talking on the phone is her favorite pastime?

No, the sentence "Talking on the phone is her favorite pastime" is not a fragment.

Here's why:

* Subject: The sentence has a clear subject: "Talking on the phone".

* Verb: The sentence has a verb: "is".

* Complete Thought: The sentence expresses a complete thought. It tells us what her favorite pastime is.

A fragment is a part of a sentence that cannot stand alone because it lacks a subject, verb, or both, or it doesn't express a complete thought.