4 moments
Birth in Babylon
· Babylon, Iraq

Wikimedia Commons · CC0 1.0 Universal Public Domain Dedication · file Hammurabi was conventionally born in the city of Babylon. The year is approximate and follows the conventional Middle Chronology. The source marks the birth year as circa; the article also states that his exact birth date is unknown.
Diplomatic meeting at Sippar
· Sippar (Tell Abu Habbah), Iraq

Wikimedia Commons · Public domain · file During the dispute over an alliance with Zimri-Lim of Mari against Elam, Hammurabi met two Mariote ambassadors at Sippar and heard their message. 1765 BC is a conventional Middle-Chronology placement for the Elam/Mari diplomatic crisis; the cited passage does not establish an exact year for this meeting.
Installed at conquered Larsa
· Larsa (Tell as-Senkereh), Iraq

Wikimedia Commons · Public domain · file After defeating Rim-Sin I and annexing Larsa, Hammurabi established himself in the city, where he was acknowledged under his expanded royal title. 1763 BC follows the conventional Middle Chronology; the absolute date of Hammurabi's reign is debated.
Death in Babylon
· Babylon, Iraq

Wikimedia Commons · Creative Commons Attribution-Share Alike 4.0 International · file Hammurabi died in Babylon in the forty-third year of his reign and was succeeded by his son Samsu-iluna. The conventional Middle Chronology dates his death to around 1750 BC; alternative Mesopotamian chronologies place the reign differently.