Properties

Label 3.3.ae_f_ad
Base Field $\F_{3}$
Dimension $3$
$p$-rank $2$

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Invariants

Base field:  $\F_{3}$
Dimension:  $3$
Weil polynomial:  $( 1 - 3 x + 3 x^{2} )( 1 - x - x^{2} - 3 x^{3} + 9 x^{4} )$
Frobenius angles:  $\pm0.126866938441$, $\pm0.166666666667$, $\pm0.718153680921$
Angle rank:  $2$ (numerical)

Newton polygon

$p$-rank:  $2$
Slopes:  $[0, 0, 1/2, 1/2, 1, 1]$

Point counts

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 5 455 12740 739375 16368400 421999760 11779638295 288061239375 7712227910660 207603952774400

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 0 4 15 108 275 793 2450 6692 19905 59539

Decomposition

1.3.ad $\times$ 2.3.ab_ab

Base change

This is a primitive isogeny class.