Abelian variety isogeny class 3.13.al_cn_ako over $\F_{13}$

• Label: 3.13.al_cn_ako
• Base field: $\F_{13}$
• Dimension: $3$
• $p$-rank: $3$
• Ordinary: yes
• Supersingular: no
• Simple: yes
• Geometrically simple: yes
• Primitive: yes
• Principally polarizable: yes
• Contains a Jacobian: yes

Invariants

Base field:	$\F_{13}$
Dimension:	$3$
L-polynomial:	$1 - 11 x + 65 x^{2} - 274 x^{3} + 845 x^{4} - 1859 x^{5} + 2197 x^{6}$
Frobenius angles:	$\pm0.0559601215895$, $\pm0.296982944631$, $\pm0.517384414518$
Angle rank:	$3$ (numerical)
Number field:	6.0.16331313488.1
Galois group:	$S_4\times C_2$

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:	$3$
Slopes:	$[0, 0, 0, 1, 1, 1]$

Point counts

Point counts of the abelian variety

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$964$	$5062928$	$10564479856$	$23047825372416$	$51132299127934644$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$3$	$179$	$2190$	$28255$	$370903$	$4825400$	$62721963$	$815647903$	$10604705358$	$137860003899$

Jacobians and polarizations

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

Decomposition and endomorphism algebra

All geometric endomorphisms are defined over $\F_{13}$.

Endomorphism algebra over $\F_{13}$

The endomorphism algebra of this simple isogeny class is 6.0.16331313488.1.

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
3.13.l_cn_ko	$2$	(not in LMFDB)