Abelian variety isogeny class 2.1024.aer_ilf over $\F_{2^{10}}$

• Label: 2.1024.aer_ilf
• Base field: $\F_{2^{10}}$
• 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:	$\F_{2^{10}}$
Dimension:	$2$
L-polynomial:	$1 - 121 x + 5699 x^{2} - 123904 x^{3} + 1048576 x^{4}$
Frobenius angles:	$\pm0.0381294656189$, $\pm0.145171135660$
Angle rank:	$2$ (numerical)
Number field:	4.0.63621537.2
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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$930251$	$1096115683551$	$1152841475142640052$	$1208924351680964989998123$	$1267650587047464261641567802941$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$904$	$1045334$	$1073667289$	$1099510292698$	$1125899895135754$	$1152921504964154231$	$1180591620740097971308$	$1208925819615287371132594$	$1237940039285387172688420777$	$1267650600228228921372860142614$

Jacobians and polarizations

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

Decomposition and endomorphism algebra

All geometric endomorphisms are defined over $\F_{2^{10}}$.

Endomorphism algebra over $\F_{2^{10}}$

The endomorphism algebra of this simple isogeny class is 4.0.63621537.2.

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
2.1024.er_ilf	$2$	(not in LMFDB)