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 $E$.

**Authors:**

**Knowl status:**

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

**Referred to by:**

**History:**(expand/hide all)

- 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

**Differences**(show/hide)