Properties

Label 2.256.acd_bwl
Base Field $\F_{2^{8}}$
Dimension $2$
Ordinary Yes
$p$-rank $2$
Principally polarizable Yes
Contains a Jacobian Yes

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Invariants

Base field:  $\F_{2^{8}}$
Dimension:  $2$
L-polynomial:  $1 - 55 x + 1259 x^{2} - 14080 x^{3} + 65536 x^{4}$
Frobenius angles:  $\pm0.0964771915839$, $\pm0.223068968241$
Angle rank:  $2$ (numerical)
Number field:  4.0.53173329.1
Galois group:  $D_{4}$

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 a Jacobian, and hence is principally polarizable.

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 52661 4261907391 281460225416804 18447077610889969419 1208927848188066205388651 79228169421608608895157438096 5192296871357367435481149985048361 340282366916870212929525420748118133459 22300745198476039386327002695290212593095164 1461501637331554786568331080456912176260495911151

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 202 65030 16776337 4295044954 1099513472752 281475001250471 72057594215876422 18446744073489011314 4722366482858086653937 1208925819615168387579350

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2^{8}}$
The endomorphism algebra of this simple isogeny class is 4.0.53173329.1.
All geometric endomorphisms are defined over $\F_{2^{8}}$.

Base change

This is a primitive isogeny class.

Twists

Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
2.256.cd_bwl$2$(not in LMFDB)