Properties

Label 2.9.ai_bi
Base Field $\F_{3^2}$
Dimension $2$
$p$-rank $2$
Principally polarizable
Contains a Jacobian

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Invariants

Base field:  $\F_{3^2}$
Dimension:  $2$
Weil polynomial:  $( 1 - 4 x + 9 x^{2} )^{2}$
Frobenius angles:  $\pm0.267720472801$, $\pm0.267720472801$
Angle rank:  $1$ (numerical)

Newton polygon

This isogeny class is ordinary.

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

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
$A(\F_{q^r})$ 36 7056 599076 45158400 3514829796 281922769296 22838210176356 1852000896614400 150086078850026916 12158100634565014416

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 2 86 818 6878 59522 530486 4774898 43023038 387398402 3486909206

Decomposition

1.9.ae 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.a_ae