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

• Label: 2.256.acf_byv
• 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:	$1 - 57 x + 1321 x^{2} - 14592 x^{3} + 65536 x^{4}$
Frobenius angles:	$\pm0.104135360699$, $\pm0.185878890687$
Angle rank:	$2$ (numerical)
Number field:	4.0.618033.2
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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$52209$	$4255398963$	$281423363274036$	$18446988037652966403$	$1208928218644825872878169$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$200$	$64930$	$16774139$	$4295024098$	$1099513809680$	$281475020911183$	$72057594705624056$	$18446744081495153794$	$4722366482933378844971$	$1208925819614823507309490$

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 4.0.618033.2.

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_byv	$2$	(not in LMFDB)