Properties

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

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Invariants

Base field:  $\F_{2^3}$
Dimension:  $2$
Weil polynomial:  $( 1 - 5 x + 8 x^{2} )^{2}$
Frobenius angles:  $\pm0.154919815756$, $\pm0.154919815756$
Angle rank:  $1$ (numerical)

Newton polygon

This isogeny class is ordinary.

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

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
$A(\F_{q^r})$ 16 3136 258064 17172736 1091905936 69244764736 4409781602704 281675802240000 18016426864880656 1152899840893573696

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -1 47 503 4191 33319 264143 2102743 16789183 134232839 1073721647

Decomposition

1.8.af 2

Base change

This isogeny class is not primitive. It is a base change from the following isogeny classes over subfields of $\F_{2^3}$.

SubfieldPrimitive Model
$\F_{2}$2.2.ab_ab
$\F_{2}$2.2.c_f