Properties

Label 5.2.ai_bi_adt_hw_amq
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:  $( 1 - x + 2 x^{2} )( 1 - 2 x + 2 x^{2} )^{2}( 1 - 3 x + 5 x^{2} - 6 x^{3} + 4 x^{4} )$
Frobenius angles:  $\pm0.123548644961$, $\pm0.25$, $\pm0.25$, $\pm0.384973271919$, $\pm0.456881978294$
Angle rank:  $2$ (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 3800 179816 1710000 35539702 1366601600 39982829098 1019710620000 31323168057272 1132739151995000

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -5 9 22 25 35 78 149 241 454 1029

Decomposition

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

Base change

This is a primitive isogeny class.