Properties

Label 3.2.ac_c_ad
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:  $\pm0.0516399385854$, $\pm0.384973271919$, $\pm0.718306605252$
Angle rank:  $1$ (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
$A(\F_{q^r})$ 2 56 224 4144 16522 175616 2570626 16783200 133677152 1073731736

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 1 5 4 17 11 38 155 257 508 1025

Decomposition

1.2.ab $\times$ 2.2.ab_ab

Base change

This is a primitive isogeny class.