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

• Label: 2.1024.aeo_idt
• 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:	$1 - 118 x + 5505 x^{2} - 120832 x^{3} + 1048576 x^{4}$
Frobenius angles:	$\pm0.0178869819368$, $\pm0.179404760049$
Angle rank:	$2$ (numerical)
Number field:	4.0.8700480.3
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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$933132$	$1096459960224$	$1152860562808730316$	$1208925028245024039803520$	$1267650599271530133712274072652$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$907$	$1045663$	$1073685067$	$1099510908031$	$1125899905992907$	$1152921504666149791$	$1180591620701633461003$	$1208925819613092962565631$	$1237940039285293915560595723$	$1267650600228225699290827519903$

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 4.0.8700480.3.

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.eo_idt	$2$	(not in LMFDB)