Properties

Label 2.27.ar_ew
Base Field $\F_{3^3}$
Dimension $2$
$p$-rank $1$
Principally polarizable
Does not contain a Jacobian

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Invariants

Base field:  $\F_{3^3}$
Dimension:  $2$
Weil polynomial:  $( 1 - 9 x + 27 x^{2} )( 1 - 8 x + 27 x^{2} )$
Frobenius angles:  $\pm0.166666666667$, $\pm0.220355751984$
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
$A(\F_{q^r})$ 380 506160 390136880 283540708800 206088548510900 150117973554044160 109420557395143818980 79766372514544339449600 58149694946299056899662640 42391150579838845858599226800

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 11 693 19820 533529 14362661 387480726 10460503127 282429286641 7625591969780 205891094718693

Decomposition

1.27.aj $\times$ 1.27.ai

Base change

This is a primitive isogeny class.