Properties

Label 4.3.ai_bc_aci_eb
Base Field $\F_{3}$
Dimension $4$
$p$-rank $2$
Does not contain a Jacobian

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Invariants

Base field:  $\F_{3}$
Dimension:  $4$
Weil polynomial:  $( 1 - 3 x + 3 x^{2} )^{2}( 1 - 2 x + x^{2} - 6 x^{3} + 9 x^{4} )$
Frobenius angles:  $\pm0.0292466093486$, $\pm0.166666666667$, $\pm0.166666666667$, $\pm0.637420057318$
Angle rank:  $1$ (numerical)

Newton polygon

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

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
$A(\F_{q^r})$ 3 2793 254016 45785649 4283299443 287570497536 23682517231971 1909235236551825 147240958586250816 11960388150768149673

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -4 2 8 86 296 746 2264 6758 19304 58082

Decomposition

1.3.ad 2 $\times$ 2.3.ac_b

Base change

This is a primitive isogeny class.