Properties

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

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Invariants

Base field:  $\F_{2}$
Dimension:  $5$
Weil polynomial:  $( 1 - 2 x + 2 x^{2} )^{3}( 1 - 3 x^{2} + 4 x^{4} )$
Frobenius angles:  $\pm0.115026728081$, $\pm0.25$, $\pm0.25$, $\pm0.25$, $\pm0.884973271919$
Angle rank:  $1$ (numerical)

Newton polygon

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

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
$A(\F_{q^r})$ 2 500 162578 4000000 74572522 1503846500 23516335306 944784000000 29061538858586 1260741700062500

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -3 -1 21 39 57 83 81 223 417 1139

Decomposition

1.2.ac 3 $\times$ 2.2.a_ad

Base change

This is a primitive isogeny class.