Properties

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

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Invariants

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

Newton polygon

This isogeny class is ordinary.

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

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
$A(\F_{q^r})$ 36 5184 311364 17438976 1065761316 68196188736 4389586477956 281540478772224 18020306184390756 1153029757503541824

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 3 79 603 4255 32523 260143 2093115 16781119 134261739 1073842639

Decomposition

1.8.ad 2

Base change

This is a primitive isogeny class.