The rabbis' own record
The Talmud is the great collection of Jewish law and teaching. The Babylonian Talmud was finished around AD 500, by rabbis who did not believe Jesus was the Messiah.
In the part on how the court carried out executions, they record this:
"On the eve of the Passover Yeshu was hanged. For forty days before the execution took place, a herald went forth and cried, 'He is going forth to be stoned because he has practised sorcery and enticed Israel to apostacy. Any one who can say anything in his favour, let him come forward and plead on his behalf.' But since nothing was brought forward in his favour he was hanged on the eve of the Passover!"
Yeshu is the Hebrew form of the name Jesus. One old manuscript of the Talmud, kept in Munich, spells it out. It calls him Yeshu the Nazarene.
Hanged
The apostles used the same word for the cross. Peter told the council in Jerusalem, "The God of our fathers hath raised up Jesus, whom you put to death, ==hanging him upon a tree==" (Acts 5:30). Luke calls the two thieves beside Jesus "these robbers who were hanging" (Luke 23:39).
On the eve of the Passover
John gives the day of the crucifixion just as precisely:
"And it was the Parasceve of the Pasch, about the sixth hour, and he saith to the Jews: Behold your king."
John 19:14
The Parasceve of the Pasch means the day of preparation for the Passover. The eve of the Passover.
An old Talmud manuscript in Florence adds three more words to the passage. Yeshu was hanged on the eve of the Passover "and the eve of Sabbath." John says the same. Jesus was taken down from the cross before sunset because "it was the Parasceve," and the next day "was a great sabbath day" (John 19:31).
Sorcery
The rabbis didn't say Jesus did no miracles. They said he did them by sorcery.
That is the exact charge the Gospels record his enemies making in his lifetime. "This man casteth not out the devils, but by Beelzebub, the prince of the devils" (Matthew 12:24). The chief priests admitted it among themselves: "What do we, for this man doth many miracles?" (John 11:47).
The Talmud also says he "enticed Israel". After the crucifixion, the chief priests went to Pilate and called him by the same name: "that seducer" (Matthew 27:63).
His disciples
A few lines later, the rabbis name his followers:
"Yeshu had five disciples, Matthai, Nakai, Nezer, Buni and Todah."
Matthai is Matthew, the tax collector who became an apostle and wrote the first Gospel (Matthew 10:3).
Cut out
When the Talmud was printed, these lines were removed. The English edition notes that the passages "have been expunged in all censored editions." They survived in the old handwritten manuscripts.
Why this is a big deal
This is the testimony of the men who rejected Jesus. They had every reason to forget him. Instead they wrote down his name, his town, the day he died, the way he died and the name of his disciple Matthew.
And they never claimed he did nothing. They admitted he did wonders, and argued over where the power came from.