Properties

Label 2.16.ai_bj
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:  $1 - 8 x + 35 x^{2} - 128 x^{3} + 256 x^{4}$
Frobenius angles:  $\pm0.100372839389$, $\pm0.484299017784$
Angle rank:  $2$ (numerical)
Number field:  4.0.66417.2
Galois group:  $D_{4}$
Jacobians:  16

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 16 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 156 66768 16554564 4252053312 1099002013356 281649882685392 72065800325865684 18446682900457813248 4722385389546620728764 1208930156277080585728848

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 9 263 4041 64879 1048089 16787639 268466025 4294953055 68719751865 1099515571943

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2^{4}}$
The endomorphism algebra of this simple isogeny class is 4.0.66417.2.
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.i_bj$2$2.256.g_alz