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

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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.

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 52211 4255666399 281429106184676 18447054251779890379 1208928758253321989787101 79228178387699640987876883600 5192296924222187926268004557127311 340282367135267632603042426568863657299 22300745199021622029842725405815230507099516 1461501637331097504390346359179335248392861470159

Point counts of the curve

$r$ 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.
TwistExtension DegreeCommon base change
2.256.cf_byx$2$(not in LMFDB)