Abelian variety isogeny class 2.101.abl_uy over $\F_{101}$

• Label: 2.101.abl_uy
• Base field: $\F_{101}$
• 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:	$\F_{101}$
Dimension:	$2$
L-polynomial:	$( 1 - 19 x + 101 x^{2} )( 1 - 18 x + 101 x^{2} )$
	$1 - 37 x + 544 x^{2} - 3737 x^{3} + 10201 x^{4}$
Frobenius angles:	$\pm0.105783363728$, $\pm0.146794250513$
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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$6972$	$101233440$	$1059997780800$	$10828633732076160$	$110463853222916990412$

Point counts of the (virtual) curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$65$	$9921$	$1028822$	$104061041$	$10510256605$	$1061522914518$	$107213570040985$	$10828567418269441$	$1093685275866613982$	$110462212563908055801$

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 $\F_{101}$.

Endomorphism algebra over $\F_{101}$

The isogeny class factors as 1.101.at $\times$ 1.101.as and its endomorphism algebra is a direct product of the endomorphism algebras for each isotypic factor. The endomorphism algebra for each factor is:

• 1.101.at : \(\Q(\sqrt{-43}) \).
• 1.101.as : \(\Q(\sqrt{-5}) \).

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
2.101.ab_afk	$2$	(not in LMFDB)
2.101.b_afk	$2$	(not in LMFDB)
2.101.bl_uy	$2$	(not in LMFDB)