Properties

Label 2.256.ace_bxj
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:  $1 - 56 x + 1283 x^{2} - 14336 x^{3} + 65536 x^{4}$
Frobenius angles:  $\pm0.0500302343671$, $\pm0.224057052788$
Angle rank:  $2$ (numerical)
Number field:  4.0.1818609.2
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
$A(\F_{q^r})$ 52428 4257782736 281423305653012 18446822057152570176 1208926333068277082769948 79228161403854251035354712784 5192296832745787864443969412491492 340282366746136495057496171539430049024 22300745197781475511556921932221564002717292 1461501637328970777225531109582020890791229917776

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 201 64967 16774137 4294985455 1099512094761 281474972765687 72057593680033113 18446744064233517919 4722366482711007032457 1208925819613030945148327

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2^{8}}$
The endomorphism algebra of this simple isogeny class is 4.0.1818609.2.
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_bxj$2$(not in LMFDB)