# Properties

 Label 2.256.acj_cdk 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: $( 1 - 16 x )^{2}( 1 - 29 x + 256 x^{2} )$ Frobenius angles: $0$, $0$, $\pm0.138932406859$ 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 $A(\F_{q^r})$ 51300 4240150200 281302071277500 18446279187751786800 1208924837639368840732500 79228161252780618124711665000 5192296858390826076353332372406700 340282366911323013946937837899494607200 22300745198339959529685902048275641048802500 1461501637329150291523852651298084571015305055000

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 196 64696 16766908 4294859056 1099510734676 281474972228968 72057594035929516 18446744073188297056 4722366482829270623428 1208925819613179435895576

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2^{8}}$
 The isogeny class factors as 1.256.abg $\times$ 1.256.abd 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.abd : $$\Q(\sqrt{-183})$$.
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.ad_aqa $2$ (not in LMFDB) 2.256.d_aqa $2$ (not in LMFDB) 2.256.cj_cdk $2$ (not in LMFDB) 2.256.an_bw $3$ (not in LMFDB)
Below is a list of all twists of this isogeny class.
 Twist Extension Degree Common base change 2.256.ad_aqa $2$ (not in LMFDB) 2.256.d_aqa $2$ (not in LMFDB) 2.256.cj_cdk $2$ (not in LMFDB) 2.256.an_bw $3$ (not in LMFDB) 2.256.abd_ts $4$ (not in LMFDB) 2.256.bd_ts $4$ (not in LMFDB) 2.256.abt_blo $6$ (not in LMFDB) 2.256.n_bw $6$ (not in LMFDB) 2.256.bt_blo $6$ (not in LMFDB)