Properties

Label 3.2.ae_l_as
Base Field $\F_{2}$
Dimension $3$
$p$-rank $2$
Does not contain a Jacobian

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Invariants

Base field:  $\F_{2}$
Dimension:  $3$
Weil polynomial:  $( 1 - 2 x + 2 x^{2} )( 1 - x + 2 x^{2} )^{2}$
Frobenius angles:  $\pm0.25$, $\pm0.384973271919$, $\pm0.384973271919$
Angle rank:  $1$ (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
$A(\F_{q^r})$ 4 320 2548 6400 19844 203840 2278532 18662400 129063844 960449600

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -1 11 23 23 19 47 139 287 491 911

Decomposition

1.2.ac $\times$ 1.2.ab 2

Base change

This is a primitive isogeny class.