Properties

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

Learn more about

Invariants

Base field:  $\F_{3}$
Dimension:  $2$
Weil polynomial:  $( 1 - 3 x + 3 x^{2} )( 1 + 3 x + 3 x^{2} )$
Frobenius angles:  $\pm0.166666666667$, $\pm0.833333333333$
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.

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 7 49 784 8281 58807 614656 4780783 44129449 387459856 3458263249

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 4 4 28 100 244 838 2188 6724 19684 58564

Decomposition

1.3.ad $\times$ 1.3.d

Base change

This is a primitive isogeny class.