Why is Ireland's ccTLD .ie?

While discussing ccTLDs with a few friends, we realized that Ireland's ccTLD is .ie. In digging in a little further, we discovered that the ccTLDs were originally assigned based on the ISO 3166-1 alpha-2 codes assigned in '74 - something which I never knew but makes perfect sense. So it follows on that Ireland's .ie TLD stems from it's ISO 3166-1 alpha-2 code also being IE. I also understand that Ireland originally went by the name Eire. But what I still can't figure out is why Ireland's original ISO 3166-1 alpha-2 designation wasn't .ei instead of .ie?

I've dug around as much as I can but I'm now at a loss - hoping someone has some historical information as to how this came about.

[EDIT] - Just to add to this, one thing I just found out was that a historical name of Ireland was "Inis Ealga" ("Noble Island") - via https://enacademic.com/dic.nsf/enwiki/739995. This is the first reference I've seen to any name that could possible align with IE. It's tenuous obviously, but thought it worth adding.