Abelian variety isogeny class 2.163.abx_bjq over $\F_{163}$

• Label: 2.163.abx_bjq
• Base field: $\F_{163}$
• Dimension: $2$
• $p$-rank: $2$
• Ordinary: yes
• Supersingular: no
• Simple: no
• Geometrically simple: no
• Primitive: yes
• Principally polarizable: yes
• Contains a Jacobian: no

Invariants

Base field:	$\F_{163}$
Dimension:	$2$
L-polynomial:	$( 1 - 25 x + 163 x^{2} )( 1 - 24 x + 163 x^{2} )$
	$1 - 49 x + 926 x^{2} - 7987 x^{3} + 26569 x^{4}$
Frobenius angles:	$\pm0.0652307277549$, $\pm0.110906256499$
Angle rank:	$2$ (numerical)
Jacobians:	$0$

This isogeny class is not simple, primitive, ordinary, and not supersingular. It is principally polarizable.

Newton polygon

This isogeny class is ordinary.

$p$-rank:	$2$
Slopes:	$[0, 0, 1, 1]$

Point counts

Point counts of the abelian variety

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$19460$	$691452720$	$18731618193680$	$498279208845297600$	$13239608729463169976300$

Point counts of the (virtual) curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$115$	$26021$	$4325260$	$705866137$	$115063380325$	$18755370981254$	$3057125310580015$	$498311415739115953$	$81224760556748015860$	$13239635967340870081061$

Jacobians and polarizations

This isogeny class is principally polarizable, but does not contain a Jacobian.

Decomposition and endomorphism algebra

All geometric endomorphisms are defined over $\F_{163}$.

Endomorphism algebra over $\F_{163}$

The isogeny class factors as 1.163.az $\times$ 1.163.ay and its endomorphism algebra is a direct product of the endomorphism algebras for each isotypic factor. The endomorphism algebra for each factor is:

• 1.163.az : \(\Q(\sqrt{-3}) \).
• 1.163.ay : \(\Q(\sqrt{-19}) \).

Base change

This is a primitive isogeny class.

Twists

Below are some of the twists of this isogeny class.

Twist	Extension degree	Common base change
2.163.ab_ako	$2$	(not in LMFDB)
2.163.b_ako	$2$	(not in LMFDB)
2.163.bx_bjq	$2$	(not in LMFDB)
2.163.aq_fe	$3$	(not in LMFDB)
2.163.ah_ade	$3$	(not in LMFDB)