Properties

Label 2.8.ag_x
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:  $1 - 6 x + 23 x^{2} - 48 x^{3} + 64 x^{4}$
Frobenius angles:  $\pm0.215051068352$, $\pm0.409556076405$
Angle rank:  $2$ (numerical)
Number field:  4.0.23616.1
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
$A(\F_{q^r})$ 34 4828 291550 17033184 1073484754 68848366300 4403498979886 281476022776704 18009637291430050 1152791641333286428

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 3 75 567 4159 32763 262635 2099751 16777279 134182251 1073620875

Decomposition

This is a simple isogeny class.

Base change

This is a primitive isogeny class.