# Properties

 Label 2.256.acg_cab Base Field $\F_{2^{8}}$ Dimension $2$ Ordinary Yes $p$-rank $2$ Principally polarizable Yes Contains a Jacobian Yes

## Invariants

 Base field: $\F_{2^{8}}$ Dimension: $2$ L-polynomial: $( 1 - 29 x + 256 x^{2} )^{2}$ Frobenius angles: $\pm0.138932406859$, $\pm0.138932406859$ Angle rank: $1$ (numerical)

This isogeny class is not simple.

## Newton polygon

This isogeny class is ordinary.

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

## Point counts

This isogeny class contains a Jacobian, and hence is principally polarizable.

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 51984 4252083264 281403980010000 18446940199617456384 1208928467354427809821584 79228178880765063447715560000 5192296935618077695800794316983184 340282367218620214654387395473948795904 22300745199447370132496450337670177013610000 1461501637332714576827161572334880512526343672384

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 199 64879 16772983 4295012959 1099514035879 281475034856143 72057595107672919 18446744089846911679 4722366483063773940103 1208925819616127743596079

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2^{8}}$
 The isogeny class factors as 1.256.abd 2 and its endomorphism algebra is $\mathrm{M}_{2}($$$\Q(\sqrt{-183})$$$)$
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.a_amr $2$ (not in LMFDB) 2.256.cg_cab $2$ (not in LMFDB) 2.256.bd_wn $3$ (not in LMFDB)
Below is a list of all twists of this isogeny class.
 Twist Extension Degree Common base change 2.256.a_amr $2$ (not in LMFDB) 2.256.cg_cab $2$ (not in LMFDB) 2.256.bd_wn $3$ (not in LMFDB) 2.256.a_mr $4$ (not in LMFDB) 2.256.abd_wn $6$ (not in LMFDB)