Faltings ratio (awaiting review)

In each isogeny class of elliptic curves defined over \(\Q\), there is a unique curve $E_{\text{min}}$ whose Néron lattice is a sublattice of the Néron lattices of all the curves in the class (G. Stevens, [MR:MR0962103]); it is the unique curve of minimal Faltings height among the curves in the isogeny class.

The Faltings ratio of each curve $E$ is the index of the Néron lattice of $E_{\text{min}}$ in that of $E$.