Can Isochron Scepter imprint a spell with X in its mana cost?

Isochron Scepter allows you to imprint an instant card with a converted mana cost (now called mana value) of 2 or less. Spells with X in their mana cost, such as Brain Freeze or Brainstorm... wait — a spell like Strength of Isolation or more relevantly Burst of Strength — yes, an instant with X in its cost can be imprinted as long as its mana value is 2 or less. When calculating mana value for the purpose of imprinting, X is treated as 0 (CR 202.3b), so a card like {X}{U} has a mana value of 1 while in hand, making it eligible.

When Isochron Scepter's activated ability creates a copy of the imprinted card and offers to cast it, the copy is cast without paying its mana cost (CR 702.97, Isochron Scepter's oracle text). Critically, because no mana is being paid, you cannot choose a value for X other than 0. CR 107.3b states that if a spell with X in its cost is cast without paying its mana cost, X must be 0 unless something else specifies otherwise.

So the imprinting itself is perfectly legal for eligible instants, but the practical result is that X-based effects will resolve with X = 0 every time you use the Scepter to cast the copy. This often makes such imprints useless or minimally useful.

Example: You imprint Drain Life (an {X}{B}{B} instant — actually a sorcery, but hypothetically) — more accurately, imagine imprinting Blaze if it were an instant with mana value ≤ 2. When you activate the Scepter, you cast the copy for free, but X = 0, so Blaze deals 0 damage. The copy is cast and resolves, but has no meaningful effect due to X being 0.

In summary: Yes, you can imprint an instant with X in its cost (provided its mana value with X=0 is 2 or less), but every time you use the Scepter, X will equal 0, per CR 107.3b.