Properties

Label 2.256.acf_bym
Base Field $\F_{2^{8}}$
Dimension $2$
Ordinary No
$p$-rank $1$
Principally polarizable Yes
Contains a Jacobian No

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Invariants

Base field:  $\F_{2^{8}}$
Dimension:  $2$
L-polynomial:  $( 1 - 16 x )^{2}( 1 - 25 x + 256 x^{2} )$
Frobenius angles:  $0$, $0$, $\pm0.214582404850$
Angle rank:  $1$ (numerical)

This isogeny class is not simple.

Newton polygon

$p$-rank:  $1$
Slopes:  $[0, 1/2, 1/2, 1]$

Point counts

This isogeny class is principally polarizable, but does not contain a Jacobian.

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 52200 4254195600 281397520567800 18446689224355860000 1208925759384596592405000 79228158916838079267562388400 5192296819596796405022210204011800 340282366662765215712021123687105960000 22300745197247632383871474958124181983676200 1461501637325860131202494079846835489815151490000

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 200 64912 16772600 4294954528 1099511573000 281474963930032 72057593497554200 18446744059713951808 4722366482597961353000 1208925819610457879065552

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2^{8}}$
The isogeny class factors as 1.256.abg $\times$ 1.256.az 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 are some of the twists of this isogeny class.
TwistExtension DegreeCommon base change
2.256.ah_alc$2$(not in LMFDB)
2.256.h_alc$2$(not in LMFDB)
2.256.cf_bym$2$(not in LMFDB)
2.256.aj_ei$3$(not in LMFDB)
Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
2.256.ah_alc$2$(not in LMFDB)
2.256.h_alc$2$(not in LMFDB)
2.256.cf_bym$2$(not in LMFDB)
2.256.aj_ei$3$(not in LMFDB)
2.256.az_ts$4$(not in LMFDB)
2.256.z_ts$4$(not in LMFDB)
2.256.abp_bjc$6$(not in LMFDB)
2.256.j_ei$6$(not in LMFDB)
2.256.bp_bjc$6$(not in LMFDB)