Properties

Label 3.2.ae_k_aq
Base Field $\F_{2}$
Dimension $3$
Ordinary No
$p$-rank $0$
Contains a Jacobian No

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Invariants

Base field:  $\F_{2}$
Dimension:  $3$
Weil polynomial:  $( 1 + 2 x^{2} )( 1 - 2 x + 2 x^{2} )^{2}$
Frobenius angles:  $\pm0.25$, $\pm0.25$, $\pm0.5$
Angle rank:  $0$ (numerical)

Newton polygon

This isogeny class is supersingular.

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

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
$A(\F_{q^r})$ 3 225 1521 5625 55473 342225 1647201 11390625 118688193 1144130625

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -1 9 17 25 49 81 97 161 449 1089

Decomposition

1.2.ac 2 $\times$ 1.2.a

Base change

This is a primitive isogeny class.