The Judeans were in captivity 70 years to the Babylonians, who had later captured Babylon. You are thinking of the Israelites, who had gone into captivity to the Assyrians 200 years earlier. This was the 70 year captivity of Nebuchadnezzar, followed by the Decree of Cyrus, and followed up by Artaxerxes
Ezra 7:1-6
After these things,
during the reign of Artaxerxes king of Persia, Ezra son of Seraiah, the son of Azariah, the son of Hilkiah, 2 the son of Shallum, the son of Zadok, the son of Ahitub, 3 the son of Amariah, the son of Azariah, ... the son of Aaron the chief priest—this
Ezra came up from Babylon. He was a teacher well versed in the Law of Moses, which the Lord, the God of Israel, had given. The king had granted him everything he asked, for the hand of the Lord his God was on him. 7 Some of the Israelites, including priests, Levites, singers, gatekeepers and temple servants, also came up to Jerusalem in the seventh year of King Artaxerxes.
8 Ezra arrived in Jerusalem in the fifth month of the seventh year of the king. 9 He had begun his journey from Babylon on the first day of the first month, and he arrived in Jerusalem on the first day of the fifth month, for the gracious hand of his God was on him. 10 For Ezra had devoted himself to the study and observance of the Law of the Lord, and to teaching its decrees and laws in Israel.
Ezra 8:1 8 These are the family heads and those registered with them who came up with me from Babylon during the reign of King Artaxerxes: NIV