Properties

Label 2.27.at_fo
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:  $( 1 - 10 x + 27 x^{2} )( 1 - 9 x + 27 x^{2} )$
Frobenius angles:  $\pm0.0877398280459$, $\pm0.166666666667$
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
$A(\F_{q^r})$ 342 480852 383719896 282467852064 205964488547802 150111152710739136 109421593343306599914 79766771079856192387200 58149770253024280653386424 42391160796642835004717823252

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 9 657 19494 531513 14354019 387463122 10460602161 282430697841 7625601845298 205891144341057

Decomposition

1.27.ak $\times$ 1.27.aj

Base change

This is a primitive isogeny class.