Properties

Label 2.8.ah_bc
Base Field $\F_{2^3}$
Dimension $2$
$p$-rank $1$
Principally polarizable
Does not contain a Jacobian

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Invariants

Base field:  $\F_{2^3}$
Dimension:  $2$
Weil polynomial:  $( 1 - 4 x + 8 x^{2} )( 1 - 3 x + 8 x^{2} )$
Frobenius angles:  $\pm0.25$, $\pm0.322067999368$
Angle rank:  $1$ (numerical)

Newton polygon

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

Point counts

This isogeny class is principally polarizable, but does not contain a Jacobian.

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 30 4680 304110 17643600 1078134150 68457593880 4389525719070 281370287671200 18015152855242230 1152975630858503400

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 2 72 590 4304 32902 261144 2093086 16770976 134223350 1073792232

Decomposition

1.8.ae $\times$ 1.8.ad

Base change

This is a primitive isogeny class.