Properties

Label 2.16.ak_bx
Base Field $\F_{2^{4}}$
Dimension $2$
Ordinary Yes
$p$-rank $2$
Principally polarizable Yes
Contains a Jacobian Yes

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Invariants

Base field:  $\F_{2^{4}}$
Dimension:  $2$
L-polynomial:  $1 - 10 x + 49 x^{2} - 160 x^{3} + 256 x^{4}$
Frobenius angles:  $\pm0.0660425289118$, $\pm0.412497962872$
Angle rank:  $2$ (numerical)
Number field:  4.0.10304.1
Galois group:  $D_{4}$
Jacobians:  12

This isogeny class is simple and geometrically simple.

Newton polygon

This isogeny class is ordinary.

$p$-rank:  $2$
Slopes:  $[0, 0, 1, 1]$

Point counts

This isogeny class contains the Jacobians of 12 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 136 64736 16734664 4257298304 1096317656776 281420217561056 72064807316490376 18447125055386607104 4722354706500636490504 1208924802784313506001376

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 7 255 4087 64959 1045527 16773951 268462327 4295055999 68719305367 1099510702975

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2^{4}}$
The endomorphism algebra of this simple isogeny class is 4.0.10304.1.
All geometric endomorphisms are defined over $\F_{2^{4}}$.

Base change

This is a primitive isogeny class.

Twists

Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
2.16.k_bx$2$2.256.ac_alb