The Talmud says in Tractate Makkot:

A Sanhedrin that effects an execution once in seven years is branded a destructive tribunal. Rabbi Eliezer ben Azariah says: Once in seventy years. Rabbi Tarfon and Rabbi Akiva say: Were we members of a Sanhedrin, no person would ever be put to death. [Thereupon] Rabban Simeon ben Gamaliel remarked, [yea] and they would also multiply shedders of blood in Israel! [Makkot 7a]

All executions were, by Roman law, to be carried out by the empire.

Whether it was the extreme brutality of the Romans or some disagreement between members of the court, something happened in 30CE that affected the Sanhedrin (the supreme court of first century Judaism) so much they physically removed themselves from the Temple so they could never again impose the death sentence. And indeed the death sentence was never again imposed.

Again, from the Talmud in Tractate Avodah Zara it says:

Forty years before the Temple was destroyed did the Sanhedrin abandon [the Temple] and held its sittings in Hanuth. Has this any legal bearing?... Capital cases ceased. Why? -- Because when the Sanhedrin saw that murderers were so prevalent that they could not be properly dealt with judicially, they said: Rather let us be exiled from place to place than pronounce them guilty [of capital offences] for it is written: And you shall do according to the sentence, which they of that place which the Lord shall choose shall tell you, which implies that it is the place that matters. [Avodah Zara 8b]

That, however, was not the only change in the Temple at that time.

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