# 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

## 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.

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

 $r$ 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: 1.256.abg : the quaternion algebra over $$\Q$$ ramified at $2$ and $\infty$. 1.256.az : $$\Q(\sqrt{-399})$$.
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.
 Twist Extension Degree Common 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.
 Twist Extension Degree Common 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)