Properties

Label 5.2.ah_ba_acn_eu_ahk
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:  $( 1 - 2 x + 2 x^{2} )^{2}( 1 - 3 x + 6 x^{2} - 9 x^{3} + 12 x^{4} - 12 x^{5} + 8 x^{6} )$
Frobenius angles:  $\pm0.147012170705$, $\pm0.25$, $\pm0.25$, $\pm0.34196271642$, $\pm0.600633654388$
Angle rank:  $3$ (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
$A(\F_{q^r})$ 3 3825 86697 3538125 78877563 994848075 26085841176 1135175563125 36400837975749 1083629820189375

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -4 8 17 36 61 59 94 268 530 983

Decomposition

1.2.ac 2 $\times$ 3.2.ad_g_aj

Base change

This is a primitive isogeny class.