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

• Label: 2.97.abi_si
• 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:	$1 - 34 x + 476 x^{2} - 3298 x^{3} + 9409 x^{4}$
Frobenius angles:	$\pm0.0231262504696$, $\pm0.240112534859$
Angle rank:	$2$ (numerical)
Number field:	4.0.291648.2
Galois group:	$D_{4}$
Jacobians:	$4$
Isomorphism classes:	4

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$6554$	$86630772$	$832381967978$	$7837490447640144$	$73742210929753160474$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$64$	$9206$	$912028$	$88529926$	$8587316764$	$832970688518$	$80798259105376$	$7837433274773374$	$760231055744994784$	$73742412671405569766$

Jacobians and polarizations

This isogeny class contains the Jacobians of 4 curves (of which all are hyperelliptic), and hence is principally polarizable:

• $y^2=64x^6+43x^5+21x^4+69x^3+15x^2+75x+40$
• $y^2=77x^6+70x^5+54x^4+78x^3+51x^2+x+18$
• $y^2=22x^6+60x^5+27x^4+7x^3+93x^2+93$
• $y^2=10x^6+46x^5+12x^4+24x^3+91x^2+x+93$

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 4.0.291648.2.

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.bi_si	$2$	(not in LMFDB)