Properties

Label 2.8.ae_h
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:  $1 - 4 x + 7 x^{2} - 32 x^{3} + 64 x^{4}$
Frobenius angles:  $\pm0.0429020132626$, $\pm0.591603161882$
Angle rank:  $2$ (numerical)
Number field:  4.0.2873.1
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
$A(\F_{q^r})$ 36 3888 225612 16127424 1076196276 68493095856 4389003840348 281501799061248 18014939308409796 1152838011359495088

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 5 63 437 3935 32845 261279 2092837 16778815 134221757 1073664063

Decomposition

This is a simple isogeny class.

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_b