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

• Label: 2.97.abl_up
• Base field: $\F_{97}$
• Dimension: $2$
• $p$-rank: $2$
• Ordinary: yes
• Supersingular: no
• Simple: yes
• Geometrically simple: yes
• Primitive: yes
• Principally polarizable: yes
• Contains a Jacobian: yes

Invariants

Base field:	$\F_{97}$
Dimension:	$2$
L-polynomial:	$1 - 37 x + 535 x^{2} - 3589 x^{3} + 9409 x^{4}$
Frobenius angles:	$\pm0.0286406432272$, $\pm0.155902322414$
Angle rank:	$2$ (numerical)
Number field:	4.0.6725.1
Galois group:	$D_{4}$
Jacobians:	$1$
Isomorphism classes:	1

This isogeny class is simple and geometrically simple, primitive, ordinary, and not supersingular. It is principally polarizable and contains a Jacobian.

Newton polygon

This isogeny class is ordinary.

$p$-rank:	$2$
Slopes:	$[0, 0, 1, 1]$

Point counts

Point counts of the abelian variety

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$6319$	$85755149$	$831116895031$	$7836505239362021$	$73742204250941926384$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$61$	$9111$	$910639$	$88518795$	$8587315986$	$832972227087$	$80798287192915$	$7837433587530579$	$760231057974527233$	$73742412675647381086$

Jacobians and polarizations

This isogeny class contains the Jacobian of 1 curve (which is hyperelliptic), and hence is principally polarizable:

• $y^2=67x^6+73x^5+67x^4+6x^3+47x^2+75x+21$

Decomposition and endomorphism algebra

All geometric endomorphisms are defined over $\F_{97}$.

Endomorphism algebra over $\F_{97}$

The endomorphism algebra of this simple isogeny class is 4.0.6725.1.

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
2.97.bl_up	$2$	(not in LMFDB)