Properties

Label 5.2.ag_q_av_i_i
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:  $( 1 - 2 x + 2 x^{2} )^{2}( 1 - 2 x + 3 x^{3} - 8 x^{5} + 8 x^{6} )$
Frobenius angles:  $\pm0.0889496890695$, $\pm0.25$, $\pm0.25$, $\pm0.297004294965$, $\pm0.823081333977$
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
$A(\F_{q^r})$ 2 800 106808 4360000 39237902 1196249600 21135172186 910446480000 35876430274568 1212843550820000

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -3 1 18 41 37 70 67 209 522 1101

Decomposition

1.2.ac 2 $\times$ 3.2.ac_a_d

Base change

This is a primitive isogeny class.