Properties

Label 2.256.ace_bxv
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:  $( 1 - 29 x + 256 x^{2} )( 1 - 27 x + 256 x^{2} )$
Frobenius angles:  $\pm0.138932406859$, $\pm0.180343027596$
Angle rank:  $2$ (numerical)

This isogeny class is not 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
$A(\F_{q^r})$ 52440 4259386560 281457157077000 18447202846853763840 1208929340281854280371000 79228179830146480954429752000 5192296923345101510910166436870760 340282367098128116471575372198373084160 22300745198744228592816255809319864274287000 1461501637329641297231930963927006709153440184000

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 201 64991 16776153 4295074111 1099514829801 281475038229023 72057594937351161 18446744083315021951 4722366482914877927433 1208925819613585586297951

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2^{8}}$
The isogeny class factors as 1.256.abd $\times$ 1.256.abb and its endomorphism algebra is a direct product of the endomorphism algebras for each isotypic factor. The endomorphism algebra for each factor is:
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.ac_akl$2$(not in LMFDB)
2.256.c_akl$2$(not in LMFDB)
2.256.ce_bxv$2$(not in LMFDB)