Properties

Label 2.256.acc_buz
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:  $1 - 54 x + 1221 x^{2} - 13824 x^{3} + 65536 x^{4}$
Frobenius angles:  $\pm0.0578961908924$, $\pm0.251397392625$
Angle rank:  $2$ (numerical)
Number field:  4.0.432625.1
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
$A(\F_{q^r})$ 52880 4264031680 281455943808080 18446886516356750080 1208925997676470576250000 79228157908502818155389586880 5192296819009005592493403996345680 340282366744286332070112248876443438080 22300745198133092741779466594451995671080080 1461501637331672318045738364425340730499095000000

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 203 65063 16776083 4295000463 1099511789723 281474960347703 72057593489396963 18446744064133220383 4722366482785464877163 1208925819615265607338823

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2^{8}}$
The endomorphism algebra of this simple isogeny class is 4.0.432625.1.
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.cc_buz$2$(not in LMFDB)