Properties

Label 5.2.ah_bd_add_go_akm
Base Field $\F_{2}$
Dimension $5$
Ordinary No
$p$-rank $3$
Contains a Jacobian No

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Invariants

Base field:  $\F_{2}$
Dimension:  $5$
Weil polynomial:  $( 1 - 2 x + 2 x^{2} )^{2}( 1 - x + 2 x^{2} )^{3}$
Frobenius angles:  $\pm0.25$, $\pm0.25$, $\pm0.384973271919$, $\pm0.384973271919$, $\pm0.384973271919$
Angle rank:  $1$ (numerical)

Newton polygon

$p$-rank:  $3$
Slopes:  $[0, 0, 0, 1/2, 1/2, 1/2, 1/2, 1, 1, 1]$

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 12800 463736 2560000 17899288 741977600 36561324472 1209323520000 32157289243352 952958093120000

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -4 14 32 30 16 38 136 286 464 854

Decomposition

1.2.ac 2 $\times$ 1.2.ab 3

Base change

This is a primitive isogeny class.