Properties

 Label 1.9.a Base Field $\F_{3^2}$ Dimension $1$ Ordinary No $p$-rank $0$ Principally polarizable Yes Contains a Jacobian Yes

Invariants

 Base field: $\F_{3^2}$ Dimension: $1$ Weil polynomial: $1 + 9 x^{2}$ Frobenius angles: $\pm0.5$ Angle rank: $0$ (numerical) Number field: $$\Q(\sqrt{-1})$$ 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 $A(\F_{q^r})$ 10 100 730 6400 59050 532900 4782970 43033600 387420490 3486902500

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 10 100 730 6400 59050 532900 4782970 43033600 387420490 3486902500

Decomposition

This is a simple isogeny class.

Base change

This is a primitive isogeny class.