Properties

Label 2.16.al_cj
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:  $1 - 11 x + 61 x^{2} - 176 x^{3} + 256 x^{4}$
Frobenius angles:  $\pm0.189901625224$, $\pm0.315486115946$
Angle rank:  $2$ (numerical)
Number field:  4.0.22625.1
Galois group:  $D_{4}$
Jacobians:  4

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 4 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 131 66155 17419856 4342480355 1101116001591 281469684850880 72055110843243491 18446752332853960355 4722376017962412943376 1208925667133961439921875

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 6 258 4251 66258 1050106 16776903 268426206 4294969218 68719615491 1099511489098

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2^{4}}$
The endomorphism algebra of this simple isogeny class is 4.0.22625.1.
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.l_cj$2$2.256.b_nx