Properties

Label 5.2.ag_s_abj_ca_acu
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:  $( 1 - x + 2 x^{2} )( 1 - 2 x + 2 x^{2} )^{2}( 1 - x - x^{2} - 2 x^{3} + 4 x^{4} )$
Frobenius angles:  $\pm0.0516399385854$, $\pm0.25$, $\pm0.25$, $\pm0.384973271919$, $\pm0.718306605252$
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
$A(\F_{q^r})$ 2 1400 37856 2590000 27773482 741977600 32824323394 849649500000 30927679563872 1128089405135000

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -3 5 12 33 27 38 123 193 444 1025

Decomposition

1.2.ac 2 $\times$ 1.2.ab $\times$ 2.2.ab_ab

Base change

This is a primitive isogeny class.