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

• Label: 2.97.abg_qx
• 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:	$1 - 32 x + 439 x^{2} - 3104 x^{3} + 9409 x^{4}$
Frobenius angles:	$\pm0.0627153889496$, $\pm0.277314930011$
Angle rank:	$2$ (numerical)
Number field:	4.0.6537872.1
Galois group:	$D_{4}$
Jacobians:	$14$
Isomorphism classes:	14

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$6713$	$87168305$	$833029622852$	$7837827491587625$	$73742088167281083753$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$66$	$9264$	$912738$	$88533732$	$8587302466$	$832970414406$	$80798263382658$	$7837433458385988$	$760231058982357666$	$73742412709167166864$

Jacobians and polarizations

This isogeny class contains the Jacobians of 14 curves (of which all are hyperelliptic), and hence is principally polarizable:

• $y^2=46x^6+91x^5+10x^4+88x^3+86x^2+48x+41$
• $y^2=43x^6+53x^5+25x^4+84x^3+40x^2+72x+6$
• $y^2=36x^6+86x^5+26x^4+87x^3+82x^2+43x+55$
• $y^2=49x^6+46x^5+83x^4+79x^3+74x^2+89x+50$
• $y^2=14x^6+20x^5+65x^4+54x^3+74x^2+14x+37$
• $y^2=49x^6+21x^5+31x^4+9x^3+73x^2+28x+20$
• $y^2=39x^6+58x^5+73x^4+21x^3+66x^2+6x+67$
• $y^2=56x^6+92x^5+79x^4+93x^3+17x^2+77x+19$
• $y^2=22x^6+3x^5+91x^4+4x^3+47x^2+83x+69$
• $y^2=13x^6+57x^5+36x^4+55x^3+16x^2+16x+91$
• $y^2=51x^6+77x^5+27x^4+69x^3+19x^2+30x+28$
• $y^2=10x^6+6x^5+36x^4+81x^2+35x+66$
• $y^2=43x^6+15x^5+64x^4+60x^3+38x^2+80x+39$
• $y^2=20x^6+69x^5+7x^4+74x^3+60x^2+78x+82$

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 4.0.6537872.1.

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.bg_qx	$2$	(not in LMFDB)