Elliptic curve invariants (reviewed)

Invariants of an elliptic curve $E$ over $\mathbb{Q}$ are its

• conductor, $N$
• discriminant, $\Delta$
• j-invariant, $j$
• endomorphism ring, $\text{End}(E)$. This is $\mathbb{Z}$ unless $E$ has CM
• Sato-Tate group, $\text{ST}(E)$. This is $SU(2)$ unless $E$ has CM