Properties

Label 2.16.aj_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:  $1 - 9 x + 45 x^{2} - 144 x^{3} + 256 x^{4}$
Frobenius angles:  $\pm0.144241903460$, $\pm0.427458851042$
Angle rank:  $2$ (numerical)
Number field:  4.0.626545.2
Galois group:  $D_{4}$
Jacobians:  12

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 12 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 149 67795 17004476 4282542355 1098935616329 281628131512000 72075181122945149 18447383044087046595 4722355873537529645036 1208924734672115319824875

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 8 266 4151 65346 1048028 16786343 268500968 4295116066 68719322351 1099510641026

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2^{4}}$
The endomorphism algebra of this simple isogeny class is 4.0.626545.2.
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.j_bt$2$2.256.j_acd