Abelian variety isogeny class 2.193.abx_bly over $\F_{193}$

• Label: 2.193.abx_bly
• Base field: $\F_{193}$
• 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:	$\F_{193}$
Dimension:	$2$
L-polynomial:	$( 1 - 25 x + 193 x^{2} )( 1 - 24 x + 193 x^{2} )$
	$1 - 49 x + 986 x^{2} - 9457 x^{3} + 37249 x^{4}$
Frobenius angles:	$\pm0.143734387197$, $\pm0.168091317575$
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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$28730$	$1371627660$	$51674805040040$	$1925200343504505600$	$71709323698739690262650$

Point counts of the (virtual) curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$145$	$36821$	$7187980$	$1387543777$	$267786748225$	$51682567977794$	$9974730695487745$	$1925122956692561473$	$371548729935091276780$	$71708904873095410243061$

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 $\F_{193}$.

Endomorphism algebra over $\F_{193}$

The isogeny class factors as 1.193.az $\times$ 1.193.ay and its endomorphism algebra is a direct product of the endomorphism algebras for each isotypic factor. The endomorphism algebra for each factor is:

• 1.193.az : \(\Q(\sqrt{-3}) \).
• 1.193.ay : \(\Q(\sqrt{-1}) \).

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
2.193.ab_aig	$2$	(not in LMFDB)
2.193.b_aig	$2$	(not in LMFDB)
2.193.bx_bly	$2$	(not in LMFDB)
2.193.aw_na	$3$	(not in LMFDB)
2.193.ab_agk	$3$	(not in LMFDB)