The Nightingale Bow is Karliah’s own bow, the ranged half of the Nightingale arsenal – a leveled bow that freezes and shocks with every arrow.
How to get it
Karliah gives it to you after you complete the Thieves Guild quest Blindsighted.
Leveled stats
Damage, value and enchantment depend on your level when you receive it. The best version arrives at level 46+: 19 damage – the same as a Daedric bow – and the “Nightingale Storm” enchantment: 30 frost damage and 15 shock damage. The lowest version does 10 frost and 5 shock.
Enchantment
Frost damage (which also slows) plus shock damage (which also drains magicka). It can’t be disenchanted.
Smithing
Ebony Ingot (Arcane Blacksmith), but no Smithing perk helps – push Smithing past 100 with gear or potions to get it beyond Flawless.
Pair it with the Nightingale Blade for the complete set.