Properties

Label 2.16.ak_bz
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:  $1 - 10 x + 51 x^{2} - 160 x^{3} + 256 x^{4}$
Frobenius angles:  $\pm0.118775077357$, $\pm0.396715540983$
Angle rank:  $2$ (numerical)
Number field:  4.0.281664.1
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
$A(\F_{q^r})$ 138 65964 16984350 4283438304 1097992070778 281509656727500 72071910946137198 18447781339996408704 4722393761144452492650 1208925442263001091952684

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 7 259 4147 65359 1047127 16779283 268488787 4295208799 68719873687 1099511284579

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2^{4}}$
The endomorphism algebra of this simple isogeny class is 4.0.281664.1.
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.k_bz$2$2.256.c_adj