The invariants of an elliptic curve $E$ over a number field $K$ are its

- conductor, $\mathfrak{N}$, which is an integral ideal of $K$ whose norm is the
**conductor norm**$N(\mathfrak{N})$ - minimal discriminant, $\mathfrak{D}$, also an integral ideal of $K$, whose norm is the
**minimal discriminant norm**$N(\mathfrak{D})$ - j-invariant, $j$
- endomorphism ring, $\text{End}(E)$
- Sato-Tate group, $\text{ST}(E)$

Each Weierstrass model for \(E\) also has a discriminant, $\Delta$, and discriminant norm, $N(\Delta)$, which are not strictly invariants of \(E\) since different models have, in general, different discriminants.

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- Review status: reviewed
- Last edited by John Cremona on 2021-01-07 09:46:15

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

- 2021-01-07 09:46:15 by John Cremona (Reviewed)
- 2018-12-18 10:25:57 by John Cremona (Reviewed)

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