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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 $E$.

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  • Review status: beta
  • Last edited by John Cremona on 2020-12-12 09:56:45
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