Properties

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

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Invariants

Base field:  $\F_{3}$
Dimension:  $3$
Weil polynomial:  $( 1 - 2 x + 3 x^{2} )( 1 - 2 x + 5 x^{2} - 6 x^{3} + 9 x^{4} )$
Frobenius angles:  $\pm0.254551732336$, $\pm0.304086723985$, $\pm0.538152604671$
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
$A(\F_{q^r})$ 14 1932 32984 633696 16738414 382350528 9420506074 270311900544 7729266422024 208447788052812

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 0 18 42 98 280 720 1960 6274 19950 59778

Decomposition

1.3.ac $\times$ 2.3.ac_f

Base change

This is a primitive isogeny class.