Conductor of an abelian variety (reviewed)

The conductor of an abelian variety $A$ over $\Q$ is a positive integer $N$ whose prime factors are the primes $p$ where $A$ has bad reduction. The power to which $p$ divides $N$ depends on the type of bad reduction; it can be expressed in terms of ramification in the $\ell$-adic representation associated to $A$ for any prime $\ell \ne p$.

The conductor of an abelian variety over a number field is defined similarly; it is an ideal that is a product of positive powers of the prime ideals where $A$ has bad reduction. The conductor of a curve $C$ over a number field is defined to be the conductor of the Jacobian of $C$.

Isogenous abelian varieties have the same conductor.