Learn more about

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 $10^{20}$.

Browse Sato-Tate groups

By weight 0 1

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.

Find a specific Sato-Tate group by label or by name

e.g. 0.1.3 or 0.1.mu(3), or or N(U(1)), or or 1.4.USp(4)