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

• Label: 2.1024.aes_inv
• 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:	$1 - 122 x + 5767 x^{2} - 124928 x^{3} + 1048576 x^{4}$
Frobenius angles:	$\pm0.0710065369012$, $\pm0.118913228236$
Angle rank:	$2$ (numerical)
Number field:	4.0.6999104.2
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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$929294$	$1096003767836$	$1152835705510503602$	$1208924196207911922915296$	$1267650589112939617298113203774$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$903$	$1045227$	$1073661915$	$1099510151295$	$1125899896970263$	$1152921505447023627$	$1180591620776184531243$	$1208925819617269078909119$	$1237940039285478711517444455$	$1267650600228232647869333803627$

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 4.0.6999104.2.

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.es_inv	$2$	(not in LMFDB)