His name comes from a game of dice: while the queen carried him, no one could defeat her, so the child was called the unconquered one. It is a small story, but it is typical — most of the middle Tirthankaras are named from something that happened during the pregnancy.
His era belongs equally to his cousin Sagara, the second universal emperor, and Sagara's sixty thousand sons. Wanting to protect Rishabha's shrine on Ashtapada, they dig a great trench around the mountain and flood it with the Ganga. The digging breaks into the realm of the nagas, whose king burns them to ash. Sagara, having lost sixty thousand sons, goes to Ajitanatha and renounces. The Hindu Puranas tell a related story of Sagara's sons and the descent of the Ganga — two traditions working the same inherited material toward different ends.

