Properties

Label 3.9.am_cq_ajm
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:  $(1-3x)^{2}(1-5x+9x^{2})(1-x+9x^{2})$
Frobenius angles:  $0.0$, $0.0$, $\pm0.186429498677$, $\pm0.446699620962$
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
$A(\F_{q^r})$ 180 475200 378181440 274903200000 204591151026900 150287004912844800 109468657674159699060 79737216841532764800000 58134800970017038512947520 42388266689166895944175080000

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -2 74 712 6386 58678 532124 4785142 43030946 387320968 3486546554

Decomposition

1.9.ag $\times$ 1.9.af $\times$ 1.9.ab

Base change

This is a primitive isogeny class.