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

• Label: 2.1024.d_absf
• 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:	$1 + 3 x - 1149 x^{2} + 3072 x^{3} + 1048576 x^{4}$
Frobenius angles:	$\pm0.170249732133$, $\pm0.861797799942$
Angle rank:	$2$ (numerical)
Number field:	4.0.126316622340433.1
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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$1050503$	$1097095959559$	$1152942534952668956$	$1208927442048880663137883$	$1267650625016731908452493777113$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$1028$	$1046270$	$1073761409$	$1099513103370$	$1125899928859238$	$1152921508595156279$	$1180591620705675129776$	$1208925819617632044174418$	$1237940039285322443249027969$	$1267650600228228879296783298830$

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 4.0.126316622340433.1.

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
2.1024.ad_absf	$2$	(not in LMFDB)