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The label of a genus 2 curve over $\Q$ has the form $N$.$s$.$D$.$n$, where

  • $N$ is the conductor,
  • $s$ is a string of letters that distinguishes this isogeny class among those with the same conductor,
  • $D$ is the absolute discriminant, and
  • $n$ is a positive integer that distinguishes the curve among other curves with the same absolute discriminant in the same isogeny class.

In particular, $N.s$ is the label of the isogeny class of the Jacobian of the curve. The values $s$ and $n$ are assigned as curves are added to the database and carry no intrinsic meaning

Knowl status:
  • Review status: reviewed
  • Last edited by Andrew Sutherland on 2021-09-18 16:47:03
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