Properties

Label 2.16.ak_cd
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:  $1 - 10 x + 55 x^{2} - 160 x^{3} + 256 x^{4}$
Frobenius angles:  $\pm0.203888329072$, $\pm0.352056944208$
Angle rank:  $2$ (numerical)
Number field:  4.0.74816.1
Galois group:  $D_{4}$
Jacobians:  8

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 8 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 142 68444 17487442 4332778976 1100087387902 281450970746204 72058606549307842 18446990633426480000 4722366284201715201262 1208923382054806888962204

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 7 267 4267 66111 1049127 16775787 268439227 4295024703 68719473847 1099509410827

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2^{4}}$
The endomorphism algebra of this simple isogeny class is 4.0.74816.1.
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_cd$2$2.256.k_mz