Sato-Tate Groups

The database currently contains all rational Sato-Tate groups of weight 1 and degree up to 4, as well as all Sato-Tate groups of weight 0 and degree 1 with component group of order at most $10^{20}$.

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By degree 1 2 3 4

By identity component  $\mathrm{SO}(1)$  $\mathrm{U}(1)$  $\mathrm{SU}(2)$  $$  $$  $\mathrm{U}(1)\times\mathrm{U}(1)$  $\mathrm{U}(1)\times\mathrm{SU}(2)$  $\mathrm{SU}(2)\times\mathrm{SU}(2)$  $\mathrm{USp}(4)$

Some of our favourite Sato-Tate groups   $N(\mathrm{U}(1))$   $\mathrm{SU}(2)$   $D_{6,2}$   $E_6$   $G_{3,3}$   $\mathrm{USp}(4)$

A random Sato-Tate group from the database.

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Weight		e.g. 1 or 0-3
Degree		e.g. 4 or 1-6
Include irrational		e.g. yes or no
Identity component		e.g. U(1) or USp(4)
Components		e.g. 1 (connected) or 4-12
Trace zero density		e.g. 0, 1/2, or 3/8
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