Properties

Label 2.8.ad_q
Base Field $\F_{2^3}$
Dimension $2$
$p$-rank $1$
Principally polarizable
Contains a Jacobian

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Invariants

Base field:  $\F_{2^3}$
Dimension:  $2$
Weil polynomial:  $( 1 - 3 x + 8 x^{2} )( 1 + 8 x^{2} )$
Frobenius angles:  $\pm0.322067999368$, $\pm0.5$
Angle rank:  $1$ (numerical)

Newton polygon

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

Point counts

This isogeny class contains a Jacobian, and hence is principally polarizable.

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 54 5832 286254 16574544 1069776774 68725005336 4393816553502 281370287671200 18017352239044086 1153046002906219752

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 6 88 558 4048 32646 262168 2095134 16770976 134239734 1073857768

Decomposition

1.8.ad $\times$ 1.8.a

Base change

This is a primitive isogeny class.