Properties

Label 2.8.ad_e
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:  $1 - 3 x + 4 x^{2} - 24 x^{3} + 64 x^{4}$
Frobenius angles:  $\pm0.117638066933$, $\pm0.631737784799$
Angle rank:  $2$ (numerical)
Number field:  4.0.90972.1
Galois group:  $D_4$

This isogeny class is simple.

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
$A(\F_{q^r})$ 42 4032 231714 16781184 1087503522 68668907328 4401742065378 281745641463552 18015742946273058 1152943150333447872

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 6 64 450 4096 33186 261952 2098914 16793344 134227746 1073761984

Decomposition

This is a simple isogeny class.

Base change

This is a primitive isogeny class.