Properties

Label 3.9.an_dd_alu
Base Field $\F_{3^2}$
Dimension $3$
$p$-rank $1$
Does not contain a Jacobian

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Invariants

Base field:  $\F_{3^2}$
Dimension:  $3$
Weil polynomial:  $(1-3x)^{2}(1-4x+9x^{2})(1-3x+9x^{2})$
Frobenius angles:  $0.0$, $0.0$, $\pm0.267720472801$, $\pm0.333333333333$
Angle rank:  $1$ (numerical)

Newton polygon

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

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
$A(\F_{q^r})$ 168 489216 410207616 285702144000 204179392052328 149138782586486784 109176804659858007912 79732347143323090944000 58148079207801761291428224 42391199039177722983801167616

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -3 75 774 6639 58557 528048 4772373 43028319 387409446 3486787755

Decomposition

1.9.ag $\times$ 1.9.ae $\times$ 1.9.ad

Base change

This is a primitive isogeny class.