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In general Sato-Tate group labels have the form $w.d.r.c.ns$, where

  • $w$ is the weight (nonnegative integer);
  • $d$ is the degree (positive integer, even if $w$ is odd);
  • $r$ is the real dimension (nonnegative integer);
  • $c$ is the number of components (positive integer);
  • $n$ is the second digit of the GAP id $[c,n]$ of the component group (positive integer);
  • $s$ is a lowercase letter (or string of lowercase letters) used to break ties; it has no intrinsic meaning.

When $w=0$ we necessarily have $r=0$ and may omit $r$. When $w=0$ and $d=1$ there is exactly one Sato-Tate group for each value of $c$ and we may omit $n$ and $s$.

Knowl status:
  • Review status: reviewed
  • Last edited by Kiran S. Kedlaya on 2018-06-20 04:32:52
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