The publication of the Nahum Commentary was followed in 1977 by that of the Qumran Temple Scroll, purporting to be direct revelation by God to Moses, and representing a rearranged and enlarged version of the Law from the first half of the second century BCE. Among the many previously unregistered rules included in it, one concerns the Jew who "delivers his people to a foreign nation", and another someone who "curses his people" among foreigners. Both are to be sentenced to the same capital punishment: "You shall hang him on a tree and he shall die." In the light of this legislation, Jannaeus simply applied to the 800 Pharisees the existing Jewish law for treason: crucifixion.

But does "to hang" (the Hebrew talah of the Dead Sea texts) mean "to crucify" rather than to hang someone by the neck? To the best of my knowledge, hanging by the neck never appears as a Jewish method of execution either in Scripture or in the Mishnah and is not a synonym for rabbinic strangling. All the three extant examples describe suicides, intended or actual: the New Testament reference, from Matthew, concerns Judas. 

To find the clue, one has to start with Deuteronomy 21:22, ordering the display of the dead body of a stoned person tied to a tree or some kind of pole. By contrast, execution by "hanging" entails the affixing of someone alive to the wooden gibbet until death ensues. Whether the criminal was attached to the tree by means of a rope or with nails is not specified. Judging from Josephus's numerous mentions of Roman executions, the Pharisees executed by Jannaeus were crucified. By his time and in his writings, late first century CE, the Greek anastaurôsai = crucify from stauros = cross, left no possible room for doubt. 

A survey of Josephus's use of the Greek verbs (stauroô and anastauroô) shows that they do not occur only apropos of executions from the Roman era, but cover the entire narrative of Jewish Antiquities. Josephus used the word to render the "hanging" of the chief baker by Pharaoh, as do also the Aramaic Targums with their translation of "to hang" by tselab. In Josephus's terminology, the Persian kings Cyrus and Artaxerxes also threaten or actually implement crucifixion. In the well-known scriptural story of the capital sentence pronounced on Haman by the Persian king, the Hebrew talah (to hang) on a 50 cubit (22.5 metre) high tree, Jewish Antiquities once more opts for the Greek verb "to crucify" as it does also in the case of Haman's sons. In Maccabees, the Syrian Greeks simply cause faithful Jews to "die"; in Josephus they crucify them. Finally in the momentous Jannaeus account the same word describes the same death penalty.