Properties

Label 2.256.ace_bxh
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:  $1 - 56 x + 1281 x^{2} - 14336 x^{3} + 65536 x^{4}$
Frobenius angles:  $\pm0.0283703195117$, $\pm0.228136732104$
Angle rank:  $2$ (numerical)
Number field:  4.0.12906000.2
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
$A(\F_{q^r})$ 52426 4257515460 281417663857066 18446758351864930560 1208925823246027437106666 79228158171191753227986808260 5192296815534979144729872482357386 340282366665953473021388812661159592960 22300745197439454658797173671405113601779466 1461501637327546550291142122250039619675516162500

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 201 64963 16773801 4294970623 1099511631081 281474961280963 72057593441185161 18446744059886787583 4722366482638581299721 1208925819611852852240323

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2^{8}}$
The endomorphism algebra of this simple isogeny class is 4.0.12906000.2.
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.ce_bxh$2$(not in LMFDB)