Properties

Label 3.3.ae_i_ao
Base Field $\F_{3}$
Dimension $3$
Ordinary No
$p$-rank $3$

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Invariants

Base field:  $\F_{3}$
Dimension:  $3$
Weil polynomial:  $( 1 - 2 x + 3 x^{2} )( 1 - 2 x + x^{2} - 6 x^{3} + 9 x^{4} )$
Frobenius angles:  $\pm0.0292466093486$, $\pm0.304086723985$, $\pm0.637420057318$
Angle rank:  $1$ (numerical)

Newton polygon

This isogeny class is ordinary.

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

Point counts

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 6 684 12312 530784 14114166 320013504 9669223122 282430166400 7552438699464 205891158689964

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 0 10 18 82 240 592 2016 6562 19494 59050

Decomposition

1.3.ac $\times$ 2.3.ac_b

Base change

This is a primitive isogeny class.