Properties

Label 2.9.ah_be
Base Field $\F_{3^2}$
Dimension $2$
Ordinary No
$p$-rank $1$
Principally polarizable Yes
Contains a Jacobian No

Learn more about

Invariants

Base field:  $\F_{3^2}$
Dimension:  $2$
Weil polynomial:  $( 1 - 4 x + 9 x^{2} )( 1 - 3 x + 9 x^{2} )$
Frobenius angles:  $\pm0.267720472801$, $\pm0.333333333333$
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
$A(\F_{q^r})$ 42 7644 606816 44640960 3486431802 281402424576 22847046425322 1852792867511040 150105608160199776 12158088943167680604

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 3 93 828 6801 59043 529506 4776747 43041441 387448812 3486905853

Decomposition

1.9.ae $\times$ 1.9.ad

Base change

This is a primitive isogeny class.