# Properties

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

## Invariants

 Base field: $\F_{2^{8}}$ Dimension: $2$ L-polynomial: $( 1 - 16 x )^{2}( 1 - 23 x + 256 x^{2} )$ Frobenius angles: $0$, $0$, $\pm0.244714587078$ 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 contains a Jacobian, and hence is principally polarizable.

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 52650 4260438000 281429750633850 18446742823911948000 1208925273843386887466250 79228154008932884017451298000 5192296795851271534032910092221850 340282366605421791073310399807017368000 22300745197359433166677167781946632578340650 1461501637327805061502453133181808780658448750000

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 202 65008 16774522 4294967008 1099511131402 281474946493648 72057593168018842 18446744056605358528 4722366482621636089642 1208925819612066687702448

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2^{8}}$
 The isogeny class factors as 1.256.abg $\times$ 1.256.ax 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.ax : $$\Q(\sqrt{-55})$$.
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.aj_aiq $2$ (not in LMFDB) 2.256.j_aiq $2$ (not in LMFDB) 2.256.cd_bwa $2$ (not in LMFDB) 2.256.ah_fo $3$ (not in LMFDB)
Below is a list of all twists of this isogeny class.
 Twist Extension Degree Common base change 2.256.aj_aiq $2$ (not in LMFDB) 2.256.j_aiq $2$ (not in LMFDB) 2.256.cd_bwa $2$ (not in LMFDB) 2.256.ah_fo $3$ (not in LMFDB) 2.256.ax_ts $4$ (not in LMFDB) 2.256.x_ts $4$ (not in LMFDB) 2.256.abn_bhw $6$ (not in LMFDB) 2.256.h_fo $6$ (not in LMFDB) 2.256.bn_bhw $6$ (not in LMFDB)