Properties

Label 2.16.ah_bd
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:  $1 - 7 x + 29 x^{2} - 112 x^{3} + 256 x^{4}$
Frobenius angles:  $\pm0.123526934512$, $\pm0.516126302719$
Angle rank:  $2$ (numerical)
Number field:  4.0.241865.1
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
$A(\F_{q^r})$ 167 67635 16499600 4261613715 1100827971587 281700640728000 72062553043324367 18446789288232935235 4722416178984729976400 1208929539981090148360875

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 10 266 4027 65026 1049830 16790663 268453930 4294977826 68720199907 1099515011426

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2^{4}}$
The endomorphism algebra of this simple isogeny class is 4.0.241865.1.
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.h_bd$2$2.256.j_aih