Properties

 Label 1.3.d Base Field $\F_{3}$ Dimension $1$ Ordinary No $p$-rank $0$ Principally polarizable Yes Contains a Jacobian Yes

Invariants

 Base field: $\F_{3}$ Dimension: $1$ Weil polynomial: $1 + 3 x + 3 x^{2}$ Frobenius angles: $\pm0.833333333333$ Angle rank: $0$ (numerical) Number field: $$\Q(\sqrt{-3})$$ Galois group: $C_2$

This isogeny class is simple.

Newton polygon

This isogeny class is supersingular.

 $p$-rank: $0$ Slopes: $[1/2, 1/2]$

Point counts

This isogeny class contains a Jacobian, and hence is principally polarizable.

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 7 7 28 91 217 784 2107 6643 19684 58807

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 7 7 28 91 217 784 2107 6643 19684 58807

Decomposition

This is a simple isogeny class.

Base change

This is a primitive isogeny class.