Properties

Label 3.2.ac_e_af
Base Field $\F_{2}$
Dimension $3$
$p$-rank $3$

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Invariants

Base field:  $\F_{2}$
Dimension:  $3$
Weil polynomial:  $( 1 - x + 2 x^{2} )( 1 - x + x^{2} - 2 x^{3} + 4 x^{4} )$
Frobenius angles:  $\pm0.197201053961$, $\pm0.384973271919$, $\pm0.652365995579$
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
$A(\F_{q^r})$ 6 216 504 7344 39666 217728 2606694 20225376 116867016 958171896

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 1 9 10 25 41 54 155 305 442 909

Decomposition

1.2.ab $\times$ 2.2.ab_b

Base change

This is a primitive isogeny class.