Properties

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

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Invariants

Base field:  $\F_{2}$
Dimension:  $3$
Weil polynomial:  $( 1 + x + 2 x^{2} )( 1 - 3 x + 5 x^{2} - 6 x^{3} + 4 x^{4} )$
Frobenius angles:  $\pm0.123548644961$, $\pm0.456881978294$, $\pm0.615026728081$
Angle rank:  $2$ (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
$A(\F_{q^r})$ 4 152 304 2736 42284 323456 2557916 20142432 132772912 1078157432

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 1 9 4 9 41 78 155 305 508 1029

Decomposition

1.2.b $\times$ 2.2.ad_f

Base change

This is a primitive isogeny class.