Properties

Label 2.16.ai_bt
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:  $1 - 8 x + 45 x^{2} - 128 x^{3} + 256 x^{4}$
Frobenius angles:  $\pm0.245740075077$, $\pm0.408506512405$
Angle rank:  $2$ (numerical)
Number field:  4.0.263952.2
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
$A(\F_{q^r})$ 166 72708 17547694 4314783552 1098998890006 281464976664612 72059936860170334 18446559206942692608 4722319155192747303814 1208923287954487848426948

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 9 283 4281 65839 1048089 16776619 268444185 4294924255 68718788025 1099509325243

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2^{4}}$
The endomorphism algebra of this simple isogeny class is 4.0.263952.2.
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_bt$2$2.256.ba_sv