"Her sword, 'Hadhafang', is attached to Asfaloth's saddle. Hadhafang means 'throng-cleaver'. It was also the sword used by Elrond in the prologue battle scenes.
The inscription on her sword reads:
aen estar Hadhafang I chatholhen
thand around dan I thang an I arwen
Idril I hel en aran Gond dolen
(This last line was omitted on the sword because they could not fit the entire inscription .)
This blade is called Hadhafang
A noble defense against the enemy throng for a noble lady
Idril, daughter of the king of the Hidden Rock (Gondolin)
The linguists who came up with this inscription have made a play on words - Arwen means 'Noble Lady' in Sindarin, so even though the blade was made for her (great-)grandmother, Idril, it includes her name!"
So it's Idril's sword! Neat. It's amazing all the research they did for those movies, all of the little details they added, and all of the time and effort put into making each piece so real.