Properties

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

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Invariants

Base field:  $\F_{3}$
Dimension:  $3$
Weil polynomial:  $( 1 + 3 x^{2} )( 1 - 2 x + 3 x^{2} )^{2}$
Frobenius angles:  $\pm0.304086723985$, $\pm0.304086723985$, $\pm0.5$
Angle rank:  $1$ (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
$A(\F_{q^r})$ 16 2304 40432 589824 14289616 366799104 9667467952 272734617600 7774705143184 210999098052864

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 0 20 48 92 240 692 2016 6332 20064 60500

Decomposition

1.3.ac 2 $\times$ 1.3.a

Base change

This is a primitive isogeny class.