For non-CM elliptic curves over Q, the Cojocaru constant C_E,j is positive except when there are coincidences of division fields, which the authors classify in several abelian families.
Hessian Elliptic Curves and Side-Channel Attacks
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The Smallest Invariant Factor of Elliptic Curves, and Coincidences
For non-CM elliptic curves over Q, the Cojocaru constant C_E,j is positive except when there are coincidences of division fields, which the authors classify in several abelian families.