What does Oeta mean in Latin?

Oeta, a proper noun, means “A mountain of Thessaly, where Hercules ascended the funeral pile”.

What is the genitive of Oeta?

The genitive singular is Oetae. Oeta is feminine, first declension.

In classical Latin, [ˈoe̯.ta]; in ecclesiastical (church) Latin, [ˈɛː.ta].

proper noun · femininefirst declension

Oeta f sg (genitive Oetae)

Classical[ˈoe̯.ta]Ecclesiastical[ˈɛː.ta]

femininesingularA mountain of Thessaly, where Hercules ascended the funeral pile

Oeta, ae, or Oetē, ēs, f., = Οἴτη,

I. the mountain range between Thessaly and Ætolia, where Hercules ascended the funeral pile, now Katavothron, Plin. 4, 7, 13, § 28; Liv. 36, 15; Luc. 8, 800; Sen. Herc. Oet. 862; Cic. Tusc. 2, 7, 19; Ov. M. 9, 165; 204; 230; id. H. 9, 147; Verg. Cul. 201.—Prov.: tibi deserit Hesperus Oeten, your wish is gratified, Verg. E. 8, 30.—Hence,

II. Oe-taeus, a, um, adj., of or belonging to Œta: in monte Oetaeo, Att. ap. Cic. N. D. 3, 16, 41: juga, Prop. 1, 13, 24: deus, i. e. Hercules, id. 4, 1, 32: robur, Luc. 7, 807; also absol. Oetaeus, Ov. Ib. 349.

Borrowed from Ancient Greek Οἴτη (Oítē).