Properties

Label 2.16.ai_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:  $( 1 - 7 x + 16 x^{2} )( 1 - x + 16 x^{2} )$
Frobenius angles:  $\pm0.160861246510$, $\pm0.460106912325$
Angle rank:  $2$ (numerical)
Jacobians:  34

This isogeny class is not 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 34 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 160 69120 16948960 4280186880 1100006644000 281712053952000 72072475250892640 18446790522338795520 4722339817060746727840 1208925767910734900928000

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 9 271 4137 65311 1049049 16791343 268490889 4294978111 68719088697 1099511580751

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2^{4}}$
The isogeny class factors as 1.16.ah $\times$ 1.16.ab and its endomorphism algebra is a direct product of the endomorphism algebras for each isotypic factor. The endomorphism algebra for each factor is:
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.ag_z$2$2.256.o_ap
2.16.g_z$2$2.256.o_ap
2.16.i_bn$2$2.256.o_ap