Properties

Label 2.16.aj_bs
Base Field $\F_{2^{4}}$
Dimension $2$
Ordinary No
$p$-rank $1$
Principally polarizable Yes
Contains a Jacobian Yes

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Invariants

Base field:  $\F_{2^{4}}$
Dimension:  $2$
L-polynomial:  $1 - 9 x + 44 x^{2} - 144 x^{3} + 256 x^{4}$
Frobenius angles:  $\pm0.126935807746$, $\pm0.434779740724$
Angle rank:  $2$ (numerical)
Number field:  4.0.40293.1
Galois group:  $D_{4}$
Jacobians:  4

This isogeny class is simple and geometrically simple.

Newton polygon

$p$-rank:  $1$
Slopes:  $[0, 1/2, 1/2, 1]$

Point counts

This isogeny class contains the Jacobians of 4 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 148 67192 16892572 4273008048 1098559096948 281621709931048 72074572237616908 18447344824842527328 4722364272956246819428 1208926286959605668281432

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 8 264 4124 65200 1047668 16785960 268498700 4295107168 68719444580 1099512052824

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2^{4}}$
The endomorphism algebra of this simple isogeny class is 4.0.40293.1.
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.j_bs$2$2.256.h_afo