Abelian variety isogeny class 2.113.abj_um over $\F_{113}$

• Label: 2.113.abj_um
• Base field: $\F_{113}$
• 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:	$\F_{113}$
Dimension:	$2$
L-polynomial:	$( 1 - 18 x + 113 x^{2} )( 1 - 17 x + 113 x^{2} )$
	$1 - 35 x + 532 x^{2} - 3955 x^{3} + 12769 x^{4}$
Frobenius angles:	$\pm0.178616545187$, $\pm0.205038125192$
Angle rank:	$2$ (numerical)
Jacobians:	$0$
Isomorphism classes:	7

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$9312$	$161023104$	$2083570913664$	$26590557364056576$	$339466447350001288032$

Point counts of the (virtual) curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$79$	$12609$	$1444018$	$163084865$	$18424878719$	$2081956728798$	$235260575910383$	$26584441862139649$	$3004041933769942354$	$339456738926992198689$

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 $\F_{113}$.

Endomorphism algebra over $\F_{113}$

The isogeny class factors as 1.113.as $\times$ 1.113.ar and its endomorphism algebra is a direct product of the endomorphism algebras for each isotypic factor. The endomorphism algebra for each factor is:

• 1.113.as : \(\Q(\sqrt{-2}) \).
• 1.113.ar : \(\Q(\sqrt{-163}) \).

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
2.113.ab_adc	$2$	(not in LMFDB)
2.113.b_adc	$2$	(not in LMFDB)
2.113.bj_um	$2$	(not in LMFDB)