# Properties

 Label 2.256.acc_bvb 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: $1 - 54 x + 1223 x^{2} - 13824 x^{3} + 65536 x^{4}$ Frobenius angles: $\pm0.0693907236630$, $\pm0.248166754731$ Angle rank: $2$ (numerical) Number field: 4.0.1551424.1 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 $A(\F_{q^r})$ 52882 4264298716 281461383713902 18446944723532711136 1208926429916870251244962 79228160386857313210216654684 5192296830571602563222885933826238 340282366789955236222451958566189299584 22300745198295987784834695475716994399282162 1461501637332271044413943804064567641365866990876

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 203 65067 16776407 4295014015 1099512182843 281474969152587 72057593649860231 18446744066608936639 4722366482819959244267 1208925819615760862182827

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2^{8}}$
 The endomorphism algebra of this simple isogeny class is 4.0.1551424.1.
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_bvb $2$ (not in LMFDB)