Properties

Label 2.16.ah_bn
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:  $1 - 7 x + 39 x^{2} - 112 x^{3} + 256 x^{4}$
Frobenius angles:  $\pm0.242342613760$, $\pm0.451721988494$
Angle rank:  $2$ (numerical)
Number field:  4.0.840105.1
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
$A(\F_{q^r})$ 177 73455 17363700 4300716795 1099724316387 281579135598000 72060185239793277 18445994569161355155 4722300860256667914300 1208925394929305799426375

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 10 286 4237 65626 1048780 16783423 268445110 4294792786 68718521797 1099511241526

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2^{4}}$
The endomorphism algebra of this simple isogeny class is 4.0.840105.1.
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_bn$2$2.256.bd_rx