# Properties

 Label 2.256.acf_byx 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: $1 - 57 x + 1323 x^{2} - 14592 x^{3} + 65536 x^{4}$ Frobenius angles: $\pm0.123591725916$, $\pm0.173135264391$ Angle rank: $2$ (numerical) Number field: 4.0.1006225.1 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 $A(\F_{q^r})$ 52211 4255666399 281429106184676 18447054251779890379 1208928758253321989787101 79228178387699640987876883600 5192296924222187926268004557127311 340282367135267632603042426568863657299 22300745199021622029842725405815230507099516 1461501637331097504390346359179335248392861470159

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 200 64934 16774481 4295039514 1099514300450 281475033104423 72057594949523180 18446744085328359154 4722366482973618272561 1208925819614790132627254

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2^{8}}$
 The endomorphism algebra of this simple isogeny class is 4.0.1006225.1.
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.cf_byx $2$ (not in LMFDB)