What is the legal test for relief by way of habeas corpus?

Relief by way of a writ of habeas corpus extends to a prisoner in custody under the authority of the United States who shows that his custody violates the Constitution, laws, or treaties of the United States. 28 U.S.C. 2241(c)(3). A federal prisoner who challenges the validity or constitutionality of his conviction must file a petition for writ of habeas corpus pursuant to 28 U.S.C. 2255. A federal prisoner challenging the manner, location, or conditions of the execution of a sentence, as petitioner does here, must bring a petition for writ of habeas corpus under 28 U.S.C. 2241. Hernandez v. Campbell, 204 F.3d 861, 864-65 (9th Cir. 2000).