Properties

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

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Invariants

Base field:  $\F_{3}$
Dimension:  $3$
Weil polynomial:  $( 1 + 3 x^{2} )( 1 - 4 x + 8 x^{2} - 12 x^{3} + 9 x^{4} )$
Frobenius angles:  $\pm0.0540867239847$, $\pm0.445913276015$, $\pm0.5$
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
$A(\F_{q^r})$ 8 1088 17528 295936 12024808 417166400 10717038424 272734617600 7513685815496 207595996716608

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 0 16 24 36 200 784 2240 6332 19392 59536

Decomposition

1.3.a $\times$ 2.3.ae_i

Base change

This is a primitive isogeny class.