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, and is related to the ramification in the $p$-torsion field of the abelian variety.

The conductor of an abelian variety over a number field is defined similarly; it is an ideal that is a product of non-trivial 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 $C$.

The conductor is an invariant of the isogeny class of an abelian variety.

**Authors:**

**Knowl status:**

- Review status: reviewed
- Last edited by Andrew Sutherland on 2017-06-30 22:35:08

**Referred to by:**

- ag.bad_prime
- g2c.169.a.169.1.bottom
- g2c.25913.a.25913.1.bottom
- g2c.277.a.top
- g2c.2916.b.11664.1.bottom
- g2c.3319.a.3319.1.bottom
- g2c.336.a.172032.1.bottom
- g2c.440509.a.440509.1.bottom
- g2c.invariants
- g2c.label
- g2c.local_invariants
- g2c.paramodular_conjecture
- rcs.rigor.g2c
- rcs.source.g2c
- lmfdb/genus2_curves/main.py (line 568)
- lmfdb/genus2_curves/templates/g2c_browse.html (line 12)
- lmfdb/genus2_curves/templates/g2c_curve.html (line 55)
- lmfdb/genus2_curves/web_g2c.py (line 572)

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

- 2017-06-30 22:35:08 by Andrew Sutherland (Reviewed)