# Properties

 Label 2.256.acc_bux 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: $1 - 54 x + 1219 x^{2} - 13824 x^{3} + 65536 x^{4}$ Frobenius angles: $\pm0.0443129142907$, $\pm0.254440268732$ Angle rank: $2$ (numerical) Number field: 4.0.80359488.2 Galois group: $D_{4}$

This isogeny class is simple and geometrically 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 $A(\F_{q^r})$ 52878 4263764652 281450503931562 18446828240506887648 1208925563061167720110398 79228155387548799915467493708 5192296806917995883852851282405818 340282366693534699422117091334047686528 22300745197929905484582320228737603219592238 1461501637330800108117488999565028100993253618732

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 203 65059 16775759 4294986895 1099511394443 281474951391475 72057593321600495 18446744061381968863 4722366482742438301835 1208925819614544132196099

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2^{8}}$
 The endomorphism algebra of this simple isogeny class is 4.0.80359488.2.
All geometric endomorphisms are defined over $\F_{2^{8}}$.

## Base change

This is a primitive isogeny class.

## Twists

Below is a list of all twists of this isogeny class.
 Twist Extension Degree Common base change 2.256.cc_bux $2$ (not in LMFDB)