Properties

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

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Invariants

Base field:  $\F_{3}$
Dimension:  $3$
Weil polynomial:  $( 1 - 3 x + 3 x^{2} )( 1 - x + 2 x^{2} - 3 x^{3} + 9 x^{4} )$
Frobenius angles:  $\pm0.166666666667$, $\pm0.235082516458$, $\pm0.648854628963$
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
$A(\F_{q^r})$ 8 896 17024 792064 19535848 396591104 10717358296 285171554304 7431198793088 204231505874816

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 0 10 24 114 320 748 2240 6626 19176 58570

Decomposition

1.3.ad $\times$ 2.3.ab_c

Base change

This is a primitive isogeny class.