When was the second year of Darius's reign?

Ezra 4:24 (ESV)

24 Then the work on the house of God that is in Jerusalem stopped, and it ceased until the second year of the reign of Darius king of Persia.

According to Persian records, the second regnal year of Darius I began on Nisan 1 (April 3) 520 BC and lasted until February 21 519 BC.1