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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- Last edited by John Cremona on 2020-12-12 09:56:45

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- 2020-12-12 09:56:45 by John Cremona
- 2020-12-12 09:19:14 by John Cremona
- 2020-12-12 09:15:47 by John Cremona

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