Properties

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

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Invariants

Base field:  $\F_{2^2}$
Dimension:  $3$
Weil polynomial:  $( 1 - 2 x )^{2}( 1 - 3 x + 4 x^{2} )( 1 - x + 4 x^{2} )$
Frobenius angles:  $0.0$, $0.0$, $\pm0.230053456163$, $\pm0.419569376745$
Angle rank:  $2$ (numerical)

Newton polygon

$p$-rank:  $2$
Slopes:  $[0, 0, 1/2, 1/2, 1, 1]$

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
$A(\F_{q^r})$ 8 3456 275576 15552000 1002369128 67500687744 4373112673112 278319151872000 17822595334324424 1147521271227129216

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -3 15 69 239 957 4023 16293 64799 259341 1043655

Decomposition

1.4.ae $\times$ 1.4.ad $\times$ 1.4.ab

Base change

This is a primitive isogeny class.