# Properties

 Label 2.3.a_g Base Field $\F_{3}$ Dimension $2$ $p$-rank $0$ Principally polarizable Does not contain a Jacobian

## Invariants

 Base field: $\F_{3}$ Dimension: $2$ Weil polynomial: $( 1 + 3 x^{2} )^{2}$ Frobenius angles: $\pm0.5$, $\pm0.5$ Angle rank: $0$ (numerical)

## Newton polygon

This isogeny class is supersingular.

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

## Point counts

This isogeny class is principally polarizable, but does not contain a Jacobian.

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 16 256 784 4096 59536 614656 4787344 40960000 387459856 3544535296

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 4 22 28 46 244 838 2188 6238 19684 60022

1.3.a 2

## Base change

This is a primitive isogeny class.