Properties

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

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Invariants

Base field:  $\F_{3^2}$
Dimension:  $3$
Weil polynomial:  $(1-3x)^{2}(1-6x+20x^{2}-54x^{3}+81x^{4})$
Frobenius angles:  $0.0$, $0.0$, $\pm0.109926884584$, $\pm0.481195587521$
Angle rank:  $2$ (numerical)

Newton polygon

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

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
$A(\F_{q^r})$ 168 435456 351180648 267718348800 203978091186408 150266670616048896 109434078654909257256 79743068221423406284800 58146737962654747754233704 42392281461536542815243207936

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -2 68 658 6212 58498 532052 4783630 43034108 387400510 3486876788

Decomposition

1.9.ag $\times$ 2.9.ag_u

Base change

This is a primitive isogeny class.