Properties

Label 3.2.af_o_ay
Base Field $\F_{2}$
Dimension $3$
Ordinary No
$p$-rank $1$
Contains a Jacobian No

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Invariants

Base field:  $\F_{2}$
Dimension:  $3$
Weil polynomial:  $( 1 - x + 2 x^{2} )( 1 - 2 x + 2 x^{2} )^{2}$
Frobenius angles:  $\pm0.25$, $\pm0.25$, $\pm0.384973271919$
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
$A(\F_{q^r})$ 2 200 2366 10000 36982 236600 1813198 14580000 119844998 1017005000

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -2 8 22 32 38 56 110 224 454 968

Decomposition

1.2.ac 2 $\times$ 1.2.ab

Base change

This is a primitive isogeny class.