The application of this epithet ‘daughter of Zeus’ to Helen is an overt reference to her divinity. On the use of Dios thugatēr / thugatēr Dios ‘daughter of Zeus’ as an epithet for goddesses, see the anchor comment at I.03.374. For more on the divinity of Helen, I epitomize from Nagy 2016.05.02§§0–4:
[§0] The picturing of Helen as a ‘daughter of Zeus’ here at O.04.227 is a most fitting description of a goddess who was already worshipped at Sparta in an era as early as the second half of the second millennium BCE—an era that marks the rise and the eventual fall of an early Greek civilization that archaeologists recognize as the Mycenaean Empire. But there is a problem with this picture: how do we square the idea of Helen as goddess of Sparta with the idea of Helen of Troy as we see her come to life in the Homeric Iliad? I hope to address this problem here by taking a second look at the idea of Helen’s ‘image-double’, the word for which in Greek was eidōlon.
[§1] Helen of Troy, as we know her in the Homeric Iliad, appears to be a woman, not a goddess. But the remarkable fact is—I spotlight its relevance from the start—that the Homeric Odyssey describes Helen here at O.04.227 by way of the epithet Dios thugatēr, which means ‘daughter of Zeus’. And I spotlight here another relevant fact that is even more remarkable: the Homeric Iliad describes Helen as Dios ekgegauia ‘daughter of Zeus’ at I.03.199, I.03.418, and the same epithet occurs also at O.04.184, O.04.219, O.23.218. But the most remarkable relevant fact of them all is that Dios thugatēr ‘daughter of Zeus’, as we see this epithet deployed elsewhere not only in the Iliad but also in the Odyssey, can be used only with reference to goddesses: Aphrodite at I.03.374 and I.05.131 and I.05.312, Athena at I.02.548 and I.04.128 and I.04.515, Artemis at O.20.061, Persephone at O.11.217, Ate at I.19.091, and the Muses at I.02.491–492 (plural) and at O.01.010 (singular). These and other facts to be brought up later lead me to argue that, although Helen appears to be a woman and not a goddess in the Iliad, she is still a goddess. And I argue further that, despite appearances as poetically created in the Iliad, Helen is recognized even there as a goddess. In terms of my argument, then, Helen is recognized as a goddess not only in Sparta but also in the Troy or ‘Ilion’ of the Iliad, the name of which epic means of course ‘the song of Ilion’. And she is a goddess in ‘the song of Ilion’ precisely because she is Helen of Sparta.
[§2] Someone may object that, even if it is a fact that you have Zeus as your father, this fact alone is not enough to make you a goddess or a god. Your mother must also be a goddess. In other words, you have to have two divine immortals as your biological parents in order to be worshipped as an immortal divinity in your own right. After all, as I myself have argued in H24H 0§5, the dominant gene in the genetic code of ancient Greek mythmaking is mortality while the recessive gene is immortality, not the other way around. In other words, if the family tree that produced you includes even one solitary mortal ancestor, that will be enough to make you mortal as well—no matter how many immortal ancestors grace your genealogy. So, what about Helen’s mother in Sparta? If she were a goddess, then the status of Helen as a goddess in her own right would be a given.
[§3] In one version of the surviving myths about Helen, the mother of Helen is in fact a goddess, named Nemesis (Cypria fragment 7 ed. Allen, by way of Athenaeus 8.334b–d). In terms of this version, then, there is no question about the divinity of Helen. But things are more complicated. There are also other versions, native even to Sparta, where the mother of Helen is not Nemesis but Leda, as we read in the wording of a Spartan song dramatized by Aristophanes in the Lysistrata (line 1314). And this Leda, as we are about to see, is a mortal woman who is impregnated by Zeus. So, I am faced with a problem here. In terms of my own argumentation concerning mortality as the dominant gene, as it were, I should expect the mortality of Leda as mother to undo the divinity of Helen as daughter of Zeus. In other words, even the paternity of immortal Zeus would not be enough to cancel the mortality of a mortal mother.
[§4] But Leda is no ordinary mortal mother, since her impregnation by Zeus produces not only Helen but also two sons who are twins, commonly known in English by their Latin names Castor and Pollux—Kastōr and Poludeukēs in the original Greek—who are also known as the Dioskouroi, meaning ‘sons of Zeus’ in Greek. See the comment on I.03.237. I argue that the mythological identity of Helen as a goddess at Sparta can best be understood by contemplating the mythological identity of these two brothers of hers, the Dioskouroi.