Properties

Label 2.8.ad_b
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:  $1 - 3 x + x^{2} - 24 x^{3} + 64 x^{4}$
Frobenius angles:  $\pm0.0112653339656$, $\pm0.655401332701$
Angle rank:  $1$ (numerical)
Number field:  \(\Q(\sqrt{-3}, \sqrt{-23})\)
Galois group:  $V_4$

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
$A(\F_{q^r})$ 39 3627 219024 16455699 1069693599 68196188736 4393814338407 281442231389475 18008492339884176 1152867381969798027

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 6 58 423 4018 32646 260143 2095134 16775266 134173719 1073691418

Decomposition

This is a simple isogeny class.

Base change

This is a primitive isogeny class.