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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: reviewed
  • Last edited by John Jones on 2020-10-26 16:55:41
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