Properties

Label 4.3.ai_bj_adw_hw
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:  $( 1 - 3 x + 3 x^{2} )( 1 - x + 3 x^{2} )( 1 - 2 x + 3 x^{2} )^{2}$
Frobenius angles:  $\pm0.166666666667$, $\pm0.304086723985$, $\pm0.304086723985$, $\pm0.406785250661$
Angle rank:  $2$ (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
$A(\F_{q^r})$ 12 15120 1455552 62899200 3380489772 264095354880 22767589553196 1889625817497600 151979936138960832 12207936683852355600

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -4 16 56 112 236 682 2180 6688 19928 59296

Decomposition

1.3.ad $\times$ 1.3.ac 2 $\times$ 1.3.ab

Base change

This is a primitive isogeny class.