Tag description says the tag is for questions about the Eisenstein Integers.
Apologies for the question.
I'd like to be a bit more informed about what they are related to, and what is the motivation.
Trying to single out what and why my self mostly gives me an almost sense of vertigo.
Links to resources should suffice.
Thanks.
One application in differential geometry is that the torus $\mathbb C/L$ where $L$ are the Eisenstein integers happens to be extremal for the Loewner torus inequality in systolic geometry.