Abelian variety isogeny class 2.191.abz_bns over $\F_{191}$

• Label: 2.191.abz_bns
• Base field: $\F_{191}$
• 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:	$\F_{191}$
Dimension:	$2$
L-polynomial:	$( 1 - 26 x + 191 x^{2} )( 1 - 25 x + 191 x^{2} )$
	$1 - 51 x + 1032 x^{2} - 9741 x^{3} + 36481 x^{4}$
Frobenius angles:	$\pm0.110219473395$, $\pm0.140267993779$
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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$27722$	$1311416932$	$48523525494968$	$1771197872375495200$	$64615240680028026608702$

Point counts of the (virtual) curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$141$	$35945$	$6963894$	$1330863801$	$254195659251$	$48551245282442$	$9273284555439381$	$1771197290600549521$	$338298681621325120074$	$64615048178513941140305$

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 $\F_{191}$.

Endomorphism algebra over $\F_{191}$

The isogeny class factors as 1.191.aba $\times$ 1.191.az and its endomorphism algebra is a direct product of the endomorphism algebras for each isotypic factor. The endomorphism algebra for each factor is:

• 1.191.aba : \(\Q(\sqrt{-22}) \).
• 1.191.az : \(\Q(\sqrt{-139}) \).

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
2.191.ab_aki	$2$	(not in LMFDB)
2.191.b_aki	$2$	(not in LMFDB)
2.191.bz_bns	$2$	(not in LMFDB)