Properties

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

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Invariants

Base field:  $\F_{3}$
Dimension:  $3$
Weil polynomial:  $( 1 - 3 x + 3 x^{2} )( 1 - 2 x + 3 x^{2} )( 1 + x + 3 x^{2} )$
Frobenius angles:  $\pm0.166666666667$, $\pm0.304086723985$, $\pm0.593214749339$
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
$A(\F_{q^r})$ 10 1260 21280 655200 18035050 386104320 10039666990 289464739200 7753580353120 205065119328300

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 0 14 30 98 300 728 2100 6722 20010 58814

Decomposition

1.3.ad $\times$ 1.3.ac $\times$ 1.3.b

Base change

This is a primitive isogeny class.