@@@ Helge Fauskanger suggested that Eldarinwa is an extended form of this word as an adjective (QQ/Eldarin). More exactly, I think it is the application of the possessive/adjectival suffix -va to the word Eldarin in its noun-sense = “Elvish language”.
Quenya
Eldarin
eldarin, elvish
eldarin
noun/adjective. of the Eldar; Elvish (language)
eldarinwë leperi ar notessi
Elvish Fingers and Numerals
quenelya
adjective. of the Elves
Eldarin adj. derived from Elda: "Eldarin, Elvish" (Silm, ÉLED). Also in the longer form Eldarinwa (pl. Eldarinwë in VT47:14, in the title Eldarinwë leperi ar notessi, "The Eldarin fingers and numerals")