Properties

Label 3.4.aj_bn_adv
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:  $( 1 - 3 x + 4 x^{2} )^{3}$
Frobenius angles:  $\pm0.230053456163$, $\pm0.230053456163$, $\pm0.230053456163$
Angle rank:  $1$ (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
$A(\F_{q^r})$ 8 4096 405224 23887872 1266723368 71163817984 4329153055592 275741910761472 17809434691540136 1148967790867173376

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -4 14 92 350 1196 4238 16124 64190 259148 1044974

Decomposition

1.4.ad 3

Base change

This is a primitive isogeny class.