Properties

Label 3.4.ah_bb_acn
Base Field $\F_{2^2}$
Dimension $3$
$p$-rank $3$
Does not contain a Jacobian

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Invariants

Base field:  $\F_{2^2}$
Dimension:  $3$
Weil polynomial:  $( 1 - x + 4 x^{2} )( 1 - 3 x + 4 x^{2} )^{2}$
Frobenius angles:  $\pm0.230053456163$, $\pm0.230053456163$, $\pm0.419569376745$
Angle rank:  $2$ (numerical)

Newton polygon

This isogeny class is ordinary.

$p$-rank:  $3$
Slopes:  $[0, 0, 0, 1, 1, 1]$

Point counts

This isogeny class does not contain a Jacobian, and it is unknown whether it is principally polarizable.

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 16 6144 416176 19906560 1128577936 70476908544 4418934239344 278588803645440 17824301688403024 1148450008526075904

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -2 22 94 302 1078 4198 16462 64862 259366 1044502

Decomposition

1.4.ad 2 $\times$ 1.4.ab

Base change

This is a primitive isogeny class.