http://destiny.wikia.com/wiki/Crux_of_Crota
You need to have the eidolon equipped while killing crota?
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Nope. I've had two so far. First time I got one I hadn't even touched my Eidolon Ally since it was upgraded from the Husk. It was also in the vault. Second one I got I didn't even have an Eidolon Ally.