Properties

Label 3.9.am_ct_akb
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:  $(1-5x+9x^{2})(1-7x+27x^{2}-63x^{3}+81x^{4})$
Frobenius angles:  $\pm0.154979380638$, $\pm0.186429498677$, $\pm0.40871325752$
Angle rank:  $3$ (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
$A(\F_{q^r})$ 195 523575 413073180 287091356175 207153608703600 150820056784987200 109663972257016588515 79800937199368136888175 58145380918891292916655740 42388245063608047407254880000

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -2 80 775 6668 59413 534005 4793668 43065332 387391465 3486544775

Decomposition

1.9.af $\times$ 2.9.ah_bb

Base change

This is a primitive isogeny class.