Properties

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

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Invariants

Base field:  $\F_{3^2}$
Dimension:  $3$
Weil polynomial:  $(1-5x+9x^{2})(1-7x+26x^{2}-63x^{3}+81x^{4})$
Frobenius angles:  $\pm0.122441590128$, $\pm0.186429498677$, $\pm0.422937410221$
Angle rank:  $3$ (numerical)

Newton polygon

This isogeny class is ordinary.

$p$-rank:  $3$
Slopes:  $[0, 0, 0, 1, 1, 1]$

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
$A(\F_{q^r})$ 190 507300 401328640 283178918400 206544537831950 150805304569036800 109666217179823392670 79800072753329094297600 58147363048038910318512640 42389865631786090577507782500

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -2 78 754 6578 59238 533952 4793766 43064866 387404674 3486678078

Decomposition

1.9.af $\times$ 2.9.ah_ba

Base change

This is a primitive isogeny class.