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

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

Invariants

Base field:	$\F_{2^{8}}$
Dimension:	$2$
L-polynomial:	$( 1 - 31 x + 256 x^{2} )^{2}$
	$1 - 62 x + 1473 x^{2} - 15872 x^{3} + 65536 x^{4}$
Frobenius angles:	$\pm0.0797861753495$, $\pm0.0797861753495$
Angle rank:	$1$ (numerical)

This isogeny class is not 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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$51076$	$4236447744$	$281274289882756$	$18446138247776845824$	$1208924379804581299596676$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$195$	$64639$	$16765251$	$4294826239$	$1099510318275$	$281474972226943$	$72057594234165315$	$18446744080940741119$	$4722366483043575319491$	$1208925819618169823473279$

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 isogeny class factors as 1.256.abf^2 and its endomorphism algebra is $\mathrm{M}_{2}($\(\Q(\sqrt{-7}) \)$)$

Base change

This is a primitive isogeny class.

Twists

Below are some of the twists of this isogeny class.

Twist	Extension degree	Common base change
2.256.a_arh	$2$	(not in LMFDB)
2.256.ck_cer	$2$	(not in LMFDB)
2.256.bf_bbd	$3$	(not in LMFDB)