What does Astyagēs mean in Latin?

Astyagēs, a proper noun, means “Astyages”.

What is the genitive of Astyagēs?

The genitive singular is Astyagis. Astyagēs is masculine, third declension.

In classical Latin, [asˈty.a.ɡeːs]; in ecclesiastical (church) Latin, [asˈtiː.a.d͡ʒes].

proper noun · masculinethird declension

Astyagēs m sg (genitive Astyagis)

Classical[asˈty.a.ɡeːs]Ecclesiastical[asˈtiː.a.d͡ʒes]

Astўăges, is, m., = Ἀστυάγης.

I. King of Media, father of Mandane, and grandfather of Cyrus, by whom he was deprived of his throne, Just. 1, 4 sq.—

II. An enemy of Perseus, changed by him to stone by means of Medusa's head, Ov. M. 5, 203.

Borrowed from Ancient Greek Ἀστυάγης (Astuágēs).