Properties

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

Learn more about

Invariants

Base field:  $\F_{2^{4}}$
Dimension:  $2$
L-polynomial:  $1 - 11 x + 57 x^{2} - 176 x^{3} + 256 x^{4}$
Frobenius angles:  $\pm0.0728689886706$, $\pm0.368631800070$
Angle rank:  $2$ (numerical)
Number field:  4.0.78057.3
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
$A(\F_{q^r})$ 127 63627 16863568 4277325075 1096735474927 281339964014400 72060071974132327 18447444892188384675 4722402949892095217488 1208926063435230833771787

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 6 250 4119 65266 1045926 16769167 268444686 4295130466 68720007399 1099511849530

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2^{4}}$
The endomorphism algebra of this simple isogeny class is 4.0.78057.3.
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_cf$2$2.256.ah_aeh