Abelian variety isogeny class 2.256.acf_byr over $\F_{2^{8}}$

• Label: 2.256.acf_byr
• 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

Invariants

Base field:	$\F_{2^{8}}$
Dimension:	$2$
L-polynomial:	$1 - 57 x + 1317 x^{2} - 14592 x^{3} + 65536 x^{4}$
Frobenius angles:	$\pm0.0716566769452$, $\pm0.201368865130$
Angle rank:	$2$ (numerical)
Number field:	4.0.15360865.2
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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$52205$	$4254864115$	$281411877547820$	$18446855403405581875$	$1208927131907351124367625$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$200$	$64922$	$16773455$	$4294993218$	$1099512821300$	$281474996013047$	$72057594191080040$	$18446744072735102818$	$4722366482815842064055$	$1208925819613815538300802$

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 4.0.15360865.2.

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_byr	$2$	(not in LMFDB)