Properties

Label 2.256.ach_cbd
Base field $\F_{2^{8}}$
Dimension $2$
$p$-rank $2$
Ordinary yes
Supersingular no
Simple yes
Geometrically simple yes
Primitive yes
Principally polarizable yes
Contains a Jacobian yes

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Invariants

Base field:  $\F_{2^{8}}$
Dimension:  $2$
L-polynomial:  $1 - 59 x + 1381 x^{2} - 15104 x^{3} + 65536 x^{4}$
Frobenius angles:  $\pm0.0938889128788$, $\pm0.152829054823$
Angle rank:  $2$ (numerical)
Number field:  4.0.472625.1
Galois group:  $D_{4}$

This isogeny class is simple and geometrically simple, primitive, ordinary, and not supersingular. It is principally polarizable and contains a Jacobian.

Newton polygon

This isogeny class is ordinary.

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

Point counts

Point counts of the abelian variety

$r$ $1$ $2$ $3$ $4$ $5$
$A(\F_{q^r})$ $51755$ $4248102155$ $281370091077680$ $18446722437716197955$ $1208927299912111402734375$

Point counts of the curve

$r$ $1$ $2$ $3$ $4$ $5$ $6$ $7$ $8$ $9$ $10$
$C(\F_{q^r})$ $198$ $64818$ $16770963$ $4294962258$ $1099512974098$ $281475015762423$ $72057594816465918$ $18446744086377871938$ $4722366483043520541483$ $1208925819616592609810698$

Jacobians and polarizations

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

Decomposition and endomorphism algebra

All geometric endomorphisms are defined over $\F_{2^{8}}$.

Endomorphism algebra over $\F_{2^{8}}$
The endomorphism algebra of this simple isogeny class is 4.0.472625.1.

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.ch_cbd$2$(not in LMFDB)