Properties

 Label 1.27.aj Base Field $\F_{3^3}$ Dimension $1$ $p$-rank $0$ Principally polarizable Contains a Jacobian

Invariants

 Base field: $\F_{3^3}$ Dimension: $1$ Weil polynomial: $1 - 9 x + 27 x^{2}$ Frobenius angles: $\pm0.166666666667$ 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 $A(\F_{q^r})$ 19 703 19684 532171 14355469 387459856 10460530351 282430067923 7625597484988 205891117745743

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 19 703 19684 532171 14355469 387459856 10460530351 282430067923 7625597484988 205891117745743

Decomposition

This is a simple isogeny class.

Base change

This is a primitive isogeny class.