"Most of these attacks would have been ruled out by better choices of curves that allow simple implementations to be secure implementations. This is the primary motivation for SafeCurves. The SafeCurves criteria are designed to ensure ECC security, not just ECDLP security."
Also you completely ignored them main part of my earlier comment. The actually widely adapted, curve25519 by djb (who's also the author of that safecurves page) with no currently known weaknesses (and needless to say, no backdoors either).