Properties

Label 5.2.ah_w_abn_bs_abw
Base Field $\F_{2}$
Dimension $5$
$p$-rank $3$
Does not contain a Jacobian

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Invariants

Base field:  $\F_{2}$
Dimension:  $5$
Weil polynomial:  $( 1 - 2 x + 2 x^{2} )^{2}( 1 - 3 x + 2 x^{2} + x^{3} + 4 x^{4} - 12 x^{5} + 8 x^{6} )$
Frobenius angles:  $\pm0.0992589862044$, $\pm0.18645529951$, $\pm0.25$, $\pm0.25$, $\pm0.757883870938$
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
$A(\F_{q^r})$ 1 725 50869 5093125 58601341 1585841075 36561324472 832099483125 34659728919361 1116318920211875

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -4 0 11 44 51 87 136 188 506 1015

Decomposition

1.2.ac 2 $\times$ 3.2.ad_c_b

Base change

This is a primitive isogeny class.