Properties

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

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Invariants

Base field:  $\F_{3}$
Dimension:  $3$
Weil polynomial:  $( 1 - x + 3 x^{2} )( 1 - 3 x + 7 x^{2} - 9 x^{3} + 9 x^{4} )$
Frobenius angles:  $\pm0.227267020856$, $\pm0.406785250661$, $\pm0.464830336654$
Angle rank:  $3$ (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
$A(\F_{q^r})$ 15 2175 37980 489375 13206000 418539600 11061938805 277049379375 7377948958140 203895357600000

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 0 20 45 76 225 785 2310 6436 19035 58475

Decomposition

1.3.ab $\times$ 2.3.ad_h

Base change

This is a primitive isogeny class.