For non-CM elliptic curves E/Q, the positivity of Cojocaru's density constant C_{E,j} is studied via adelic Galois representations, with experimental evidence linking vanishing to coincidences of division fields.
Serre’s constant of elliptic curves over the rationals
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The Smallest Invariant Factor of Elliptic Curves, and Coincidences
For non-CM elliptic curves E/Q, the positivity of Cojocaru's density constant C_{E,j} is studied via adelic Galois representations, with experimental evidence linking vanishing to coincidences of division fields.