Jesus would support capital punishment in some instances.

In Geneva, on 28th April 2005, there was a call for a moratorium on corporal punishment, stoning and death penalty. This was, however, rejected by the Legal Research Commission of the Al-Azhar University in Cairo, the world's leading Islamic learning centre.

There include several different forms of capital punishment....

This article examines the Islamic position with regards to the ethics of capital punishment.
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In the United States only 38 states have capital punishment statutes.

Critics charge that executions are violations of the “cruel and unusual punishment” provision of the Eighth Amendment; while supporters of the death penalty counter that this clause was not intended to prohibit legal executions.

In the USA capital punishment costs a great deal.

Taking the teachings of the largest Christian denomination (Catholic) as a starting point, some say that the presentation of capital punishment in the Catechism of 1992 (#2266) differs surely in restrictiveness from the teaching of the Catechism of 1566.

This should not be used to indicate that Jesus rejected capital punishment in all instances.
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Capital punishment by country - Wikipedia

Dr., given that the current position of the Church, as reflected in the Catechism, is that as a practical matter capital punishment may only be used when absolutely necessary because there is no other way to prevent the offender from killing innocents, could you please answer the question how Catholic teaching concerning self-defense, military action, or police action to prevent the killing of innocents by an attacker can stand if Pope Francis is right that killing another human being is always wrong, always against the Gospel, and the taking of a human life is within the sole province of God alone? I realize that you have no obligation to engage me, but you have done so in the comments to related articles, and your answer has essentially been” “Because they’re different”. Well, that does not cut it. They are not different in principle. One who acts in self-defense kills to protect the innocent. The military kills to protect the innocent from invaders who may kill, rape or enslave them. The police kill to protect themselves or innocents from imminent harm or death. Under the justification given by Pope Francis the principle involved is exactly the same The only way to maintain the teaching that permits self-defense, military action and police action if capital punishment is impermissible even to protect innocents from death, is to accept that it is okay for the Church’s teaching to be incoherent.

BBC - Ethics - Capital punishment: Introduction

Cardinal Avery Dulles was an opponent of capital punishment, yet as a matter of principle, he clearly acknowledged it as permitted under Catholic moral theology. Cardinal Dulles is well regarded as a Catholic moral theologian.

The abolition of capital punishment in Europe

Many supporters of capital punishment cite retribution as being a justification for the death penalty; however, no matter what the circumstance, murder is never justified.

Constraints on the use of threatened punishments ..

There has been a third development concurrent with the two outlinedabove, far less influential in the formation of actual penalty policyeven if it is of equal theoretical importance (Harding 1989). We referto the reconceptualization of the practice of punishment arising fromthe work of Michel Foucault in the mid-1970s. Foucault invited us toview the practice of punishment under law as subject to general forcesin society that reflect the dominant forms of social and politicalpower—the power to threaten, coerce, suppress, destroy, transform—that prevail in any given epoch. And he also cultivated a deepsuspicion toward the claims that contemporary society had significantlyhumanized the forms of punishment by abandoning the savage corporalbrutality that prevailed in the bad old days, in favor of the hiddenconcrete-and-steel carceral system of the modern era (Foucault1977).

Why is nitrogen asphyxiation not used in capital punishment?

So I find it hypocritical that the same countries who have abolished capital punishment because it is "barbaric" to defend public safety that way are at the same time prepared to enforce political power and defend their territorial claims through infinitely more violence and bloodshed than the death penalty would ever require.