Properties

Label 2.16.ah_bc
Base Field $\F_{2^{4}}$
Dimension $2$
Ordinary No
$p$-rank $1$
Principally polarizable Yes
Contains a Jacobian Yes

Learn more about

Invariants

Base field:  $\F_{2^{4}}$
Dimension:  $2$
L-polynomial:  $1 - 7 x + 28 x^{2} - 112 x^{3} + 256 x^{4}$
Frobenius angles:  $\pm0.109519428602$, $\pm0.521148502204$
Angle rank:  $2$ (numerical)
Number field:  4.0.122525.1
Galois group:  $D_{4}$
Jacobians:  4

This isogeny class is simple and geometrically simple.

Newton polygon

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

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
$A(\F_{q^r})$ 166 67064 16414246 4256283824 1100534194126 281666819935400 72060185424422326 18446779660990619744 4722422758159647276766 1208929838474774534669784

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 10 264 4006 64944 1049550 16788648 268445110 4294975584 68720295646 1099515282904

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2^{4}}$
The endomorphism algebra of this simple isogeny class is 4.0.122525.1.
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_bc$2$2.256.h_akm