Properties

Label 2.8.ac_ad
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:  $1 - 2 x - 3 x^{2} - 16 x^{3} + 64 x^{4}$
Frobenius angles:  $\pm0.0815683182843$, $\pm0.710356941346$
Angle rank:  $2$ (numerical)
Number field:  4.0.1025.1
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
$A(\F_{q^r})$ 44 3520 226556 16966400 1068504844 68528658880 4405447115036 281463685606400 18015461395303724 1153047084266968000

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 7 55 439 4143 32607 261415 2100679 16776543 134225647 1073858775

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.b_d