Properties

Label 3.3.af_p_abe
Base Field $\F_{3}$
Dimension $3$
$p$-rank $1$
Does not contain a Jacobian

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Invariants

Base field:  $\F_{3}$
Dimension:  $3$
Weil polynomial:  $( 1 - 3 x + 3 x^{2} )( 1 - 2 x + 3 x^{2} )( 1 + 3 x^{2} )$
Frobenius angles:  $\pm0.166666666667$, $\pm0.304086723985$, $\pm0.5$
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
$A(\F_{q^r})$ 8 1344 29792 559104 16002008 420424704 10435530344 277539225600 7700377178144 208429482617664

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -1 15 38 87 269 792 2183 6447 19874 59775

Decomposition

1.3.ad $\times$ 1.3.ac $\times$ 1.3.a

Base change

This is a primitive isogeny class.