show · ec.local_root_number all knowls · up · search:

The local root number of an elliptic curve $E$ over a number field at a prime $\mathfrak p$ is the sign of the local functional equation of $E$. This is equal to $+1$ at primes of good or non-split multiplicative reduction, $-1$ at primes of split multiplicative reduction, and at primes of additive reduction is $\pm1$ with no simple characterization.

For an elliptic curve defined over $\Q$, the root number at a prime $p$ is also equal to the eigenvalue of the associated Atkin-Lehner involution for the associated modular form.

Knowl status:
  • Review status: beta
  • Last edited by John Cremona on 2020-03-16 13:01:52
Referred to by:
History: (expand/hide all) Differences (show/hide)