Properties

Label 2.8.ad_r
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:  $1 - 3 x + 17 x^{2} - 24 x^{3} + 64 x^{4}$
Frobenius angles:  $\pm0.346842152344$, $\pm0.478490494564$
Angle rank:  $2$ (numerical)
Number field:  4.0.20025.1
Galois group:  $D_4$

This isogeny class is simple.

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
$A(\F_{q^r})$ 55 5995 291280 16456275 1061941375 68705961280 4399452842455 281461561546275 18015507400150480 1152983381458904875

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 6 90 567 4018 32406 262095 2097822 16776418 134225991 1073799450

Decomposition

This is a simple isogeny class.

Base change

This is a primitive isogeny class.