Properties

Label 2.256.acd_bwj
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:  $1 - 55 x + 1257 x^{2} - 14080 x^{3} + 65536 x^{4}$
Frobenius angles:  $\pm0.0854412706717$, $\pm0.227850675283$
Angle rank:  $2$ (numerical)
Number field:  4.0.794025.3
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
$A(\F_{q^r})$ 52659 4261640211 281454684479424 18447016895039614275 1208927385567873129763179 79228166719099687418808251136 5192296858898357228009800717155219 340282366872789923180196189995456734275 22300745198375247831153247039384697791971264 1461501637331583968822110182836950589233583414691

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 202 65026 16776007 4295030818 1099513052002 281474991649231 72057594042972922 18446744071099414018 4722366482836743211927 1208925819615192526573906

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2^{8}}$
The endomorphism algebra of this simple isogeny class is 4.0.794025.3.
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_bwj$2$(not in LMFDB)