http://destiny.wikia.com/wiki/Crux_of_Crota
You need to have the eidolon equipped while killing crota?
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Don't need it at all, I have Nechrochasm in my vault with 2 Husks no ally and crux dropped a second time. I didn't have glowhoo equipped or anything! What did I do to deserve a second one? RNG must hate me FML