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

• Label: 2.256.acf_byp
• 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:	$1 - 57 x + 1315 x^{2} - 14592 x^{3} + 65536 x^{4}$
Frobenius angles:	$\pm0.0539555453686$, $\pm0.207165299693$
Angle rank:	$2$ (numerical)
Number field:	4.0.14994657.1
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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$52203$	$4254596703$	$281406134732148$	$18446788983284614827$	$1208926584778371253287933$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$200$	$64918$	$16773113$	$4294977754$	$1099512323690$	$281474983307959$	$72057593920396844$	$18446744067804279730$	$4722366482738258579849$	$1208925819612758194615318$

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 4.0.14994657.1.

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_byp	$2$	(not in LMFDB)