Properties

Label 2.9.ag_bb
Base Field $\F_{3^2}$
Dimension $2$
Ordinary No
$p$-rank $0$
Principally polarizable Yes
Contains a Jacobian Yes

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Invariants

Base field:  $\F_{3^2}$
Dimension:  $2$
Weil polynomial:  $( 1 - 3 x + 9 x^{2} )^{2}$
Frobenius angles:  $\pm0.333333333333$, $\pm0.333333333333$
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 contains a Jacobian, and hence is principally polarizable.

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 49 8281 614656 44129449 3458263249 280883040256 22855886093089 1853585177078089 150125140011540736 12158077251781589401

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 4 100 838 6724 58564 528526 4778596 43059844 387499222 3486902500

Decomposition

1.9.ad 2

Base change

This isogeny class is not primitive. It is a base change from the following isogeny classes over subfields of $\F_{3^2}$.

SubfieldPrimitive Model
$\F_{3}$2.3.g_p
$\F_{3}$2.3.a_ad
$\F_{3}$2.3.ag_p