Properties

Label 2.9.ak_bq
Base Field $\F_{3^2}$
Dimension $2$
$p$-rank $1$
Principally polarizable
Does not contain a Jacobian

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Invariants

Base field:  $\F_{3^2}$
Dimension:  $2$
Weil polynomial:  $( 1 - 3 x )^{2}( 1 - 4 x + 9 x^{2} )$
Frobenius angles:  $0.0$, $0.0$, $\pm0.267720472801$
Angle rank:  $1$ (numerical)

Newton polygon

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

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
$A(\F_{q^r})$ 24 5376 523224 43008000 3472025304 281402424576 22836594896664 1851945811968000 150075106639697304 12157471258716892416

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 0 66 720 6558 58800 529506 4774560 43021758 387370080 3486728706

Decomposition

1.9.ag $\times$ 1.9.ae

Base change

This is a primitive isogeny class.