Properties

Label 5.2.ag_r_abd_bj_abq
Base Field $\F_{2}$
Dimension $5$
$p$-rank $4$
Does not contain a Jacobian

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Invariants

Base field:  $\F_{2}$
Dimension:  $5$
Weil polynomial:  $( 1 - 2 x + 2 x^{2} )( 1 - x + 2 x^{2} )( 1 - 3 x + 2 x^{2} + x^{3} + 4 x^{4} - 12 x^{5} + 8 x^{6} )$
Frobenius angles:  $\pm0.0992589862044$, $\pm0.18645529951$, $\pm0.25$, $\pm0.384973271919$, $\pm0.757883870938$
Angle rank:  $1$ (numerical)

Newton polygon

$p$-rank:  $4$
Slopes:  $[0, 0, 0, 0, 1/2, 1/2, 1, 1, 1, 1]$

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 1160 54782 3259600 31444622 1366263080 45944319248 1065087338400 37325861913158 1054240697331800

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -3 3 12 35 32 78 165 251 543 958

Decomposition

1.2.ac $\times$ 1.2.ab $\times$ 3.2.ad_c_b

Base change

This is a primitive isogeny class.