Properties

Label 4.3.aj_bq_aev_jy
Base Field $\F_{3}$
Dimension $4$
$p$-rank $3$
Does not contain a Jacobian

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Invariants

Base field:  $\F_{3}$
Dimension:  $4$
Weil polynomial:  $( 1 - 3 x + 3 x^{2} )( 1 - 2 x + 3 x^{2} )^{3}$
Frobenius angles:  $\pm0.166666666667$, $\pm0.304086723985$, $\pm0.304086723985$, $\pm0.304086723985$
Angle rank:  $1$ (numerical)

Newton polygon

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

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
$A(\F_{q^r})$ 8 12096 1536416 80510976 3840744248 250890587136 21073303936952 1848011586011136 154514490015638816 12407390297278675776

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -5 13 58 133 265 646 2011 6541 20254 60253

Decomposition

1.3.ad $\times$ 1.3.ac 3

Base change

This is a primitive isogeny class.