Properties

Label 2.8.ah_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:  $1 - 7 x + 25 x^{2} - 56 x^{3} + 64 x^{4}$
Frobenius angles:  $\pm0.113218980851$, $\pm0.403003401001$
Angle rank:  $2$ (numerical)
Number field:  4.0.19097.1
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
$A(\F_{q^r})$ 27 4131 269568 16528131 1064375667 68794831872 4408024115907 281711299194243 18016294529316096 1152915834558818691

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 2 66 527 4034 32482 262431 2101906 16791298 134231855 1073736546

Decomposition

This is a simple isogeny class.

Base change

This is a primitive isogeny class.