Board Thread:Questions and Answers/@comment-24.62.142.87-20140331201702/@comment-114.185.0.9-20150531015437

The Elucidator is a 魔剣. This could be translated as "magic sword", but the more accurate term would be "cursed sword". The Elucidator was an item Kirito got from a demon-like boss, so it makes sense that the sword is "cursed" or has a bit of demon's spirit infused in it. As for whether the sword itself is magical, the sword could be described that way because of its firepower, but SAO doesn't have magic so that expression is a bit weird.