Properties

Label 5.3.ak_bu_afa_kh_asg
Base Field $\F_{3}$
Dimension $5$
$p$-rank $3$
Does not contain a Jacobian

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Invariants

Base field:  $\F_{3}$
Dimension:  $5$
Weil polynomial:  $(1-3x+3x^{2})^{2}(1-4x+7x^{2}-10x^{3}+21x^{4}-36x^{5}+27x^{6})$
Frobenius angles:  $\pm0.0823229705598$, $\pm0.166666666667$, $\pm0.166666666667$, $\pm0.256885878434$, $\pm0.66802383947$
Angle rank:  $3$ (numerical)

Newton polygon

$p$-rank:  $3$
Slopes:  $[0, 0, 0, 1/2, 1/2, 1/2, 1/2, 1, 1, 1]$

Point counts

This isogeny class does not contain a Jacobian, and it is unknown whether it is principally polarizable.

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 6 31164 10174752 5498451504 1180323629166 219000710863872 53780290269137466 12452327197593244416 2918128558013027575776 721479899176512815392284

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -6 2 18 118 324 776 2346 6718 19440 59342

Decomposition

1.3.ad 2 $\times$ 3.3.ae_h_ak

Base change

This is a primitive isogeny class.