The conspirators were hanged for 'high treason'.
He is guilty of 'treason'.
(..) Baelor! Traitor! Traitor! I am Eddard Stark... Lord of Winterfell... and Hand of the King. I come before you to confess my treason... in the sight of gods and men. I betrayed the faith of my king... and the trust of my friend Robert. I swore to protect and defend his children. (..)2011 TvShow: Game of Thrones Title: Baelor Season: 1 Episode 9
(..) murdered my king, who butchered my men, who crippled my son? I want you to serve the realm! Tell the queen you will confess your vile treason, tell your son to lay down his sword and proclaim Joffrey as the true heir. Cersei knows you as a man of honor. If you give her the peace she needs, (..)2011 TvShow: Game of Thrones Title: Baelor Season: 1 Episode 9