# Properties

 Label 2.256.acl_cfw 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: $( 1 - 16 x )^{2}( 1 - 31 x + 256 x^{2} )$ Frobenius angles: $0$, $0$, $\pm0.0797861753495$ 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 $A(\F_{q^r})$ 50850 4232347200 281237242226850 18445878221841820800 1208922793868854295921250 79228152438505363164788280000 5192296826919398151796185684847650 340282366829178089486626309886229715200 22300745198292266885198135706553632988423650 1461501637330384653068481681655718505866236680000

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 194 64576 16763042 4294765696 1099508875874 281474940914368 72057593599175714 18446744068735211776 4722366482819171313122 1208925819614200475834176

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2^{8}}$
 The isogeny class factors as 1.256.abg $\times$ 1.256.abf 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.abf : $$\Q(\sqrt{-7})$$.
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.ab_asm $2$ (not in LMFDB) 2.256.b_asm $2$ (not in LMFDB) 2.256.cl_cfw $2$ (not in LMFDB) 2.256.ap_q $3$ (not in LMFDB)
Below is a list of all twists of this isogeny class.
 Twist Extension Degree Common base change 2.256.ab_asm $2$ (not in LMFDB) 2.256.b_asm $2$ (not in LMFDB) 2.256.cl_cfw $2$ (not in LMFDB) 2.256.ap_q $3$ (not in LMFDB) 2.256.abf_ts $4$ (not in LMFDB) 2.256.bf_ts $4$ (not in LMFDB) 2.256.abv_bmu $6$ (not in LMFDB) 2.256.p_q $6$ (not in LMFDB) 2.256.bv_bmu $6$ (not in LMFDB)