Properties

Label 3.4.aj_bm_ads
Base Field $\F_{2^2}$
Dimension $3$
$p$-rank $1$
Does not contain a Jacobian

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Invariants

Base field:  $\F_{2^2}$
Dimension:  $3$
Weil polynomial:  $( 1 - 2 x )^{2}( 1 - 3 x + 4 x^{2} )( 1 - 2 x + 4 x^{2} )$
Frobenius angles:  $0.0$, $0.0$, $\pm0.230053456163$, $\pm0.333333333333$
Angle rank:  $1$ (numerical)

Newton polygon

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

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
$A(\F_{q^r})$ 6 3024 293706 17690400 1032523386 65280270384 4273484775594 278458819329600 17945679556246554 1150477478165396304

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -4 12 74 272 986 3888 15914 64832 261146 1046352

Decomposition

1.4.ae $\times$ 1.4.ad $\times$ 1.4.ac

Base change

This is a primitive isogeny class.