Abelian variety isogeny class 2.97.abl_uq over $\F_{97}$

• Label: 2.97.abl_uq
• Base field: $\F_{97}$
• 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:	$\F_{97}$
Dimension:	$2$
L-polynomial:	$( 1 - 19 x + 97 x^{2} )( 1 - 18 x + 97 x^{2} )$
	$1 - 37 x + 536 x^{2} - 3589 x^{3} + 9409 x^{4}$
Frobenius angles:	$\pm0.0849741350078$, $\pm0.133124938748$
Angle rank:	$2$ (numerical)
Jacobians:	$0$
Isomorphism classes:	8

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$6320$	$85775040$	$831218635520$	$7836800504083200$	$73742831790640775600$

Point counts of the (virtual) curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$61$	$9113$	$910750$	$88522129$	$8587389061$	$832973533886$	$80798307321877$	$7837433862532321$	$760231061360292190$	$73742412713473769993$

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 $\F_{97}$.

Endomorphism algebra over $\F_{97}$

The isogeny class factors as 1.97.at $\times$ 1.97.as and its endomorphism algebra is a direct product of the endomorphism algebras for each isotypic factor. The endomorphism algebra for each factor is:

• 1.97.at : \(\Q(\sqrt{-3}) \).
• 1.97.as : \(\Q(\sqrt{-1}) \).

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
2.97.ab_afs	$2$	(not in LMFDB)
2.97.b_afs	$2$	(not in LMFDB)
2.97.bl_uq	$2$	(not in LMFDB)
2.97.an_ea	$3$	(not in LMFDB)
2.97.ae_acg	$3$	(not in LMFDB)