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

• Label: 2.97.abh_rx
• 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:	$1 - 33 x + 465 x^{2} - 3201 x^{3} + 9409 x^{4}$
Frobenius angles:	$\pm0.147588620278$, $\pm0.214760304335$
Angle rank:	$2$ (numerical)
Number field:	4.0.293725.1
Galois group:	$D_{4}$
Jacobians:	$12$

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$6641$	$87056869$	$833425318001$	$7839405673741381$	$73745043650003653136$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$65$	$9251$	$913169$	$88551555$	$8587646630$	$832974838787$	$80798302170833$	$7837433631623299$	$760231057845102113$	$73742412675431629886$

Jacobians and polarizations

This isogeny class is principally polarizable and contains the Jacobians of 12 curves (of which all are hyperelliptic):

• $y^2=86 x^6+81 x^5+46 x^4+36 x^3+62 x^2+90 x+70$
• $y^2=49 x^6+47 x^5+90 x^4+69 x^3+67 x^2+79 x+70$
• $y^2=71 x^6+13 x^5+19 x^4+77 x^3+20 x^2+76 x+42$
• $y^2=60 x^6+65 x^5+54 x^4+10 x^3+84 x^2+91 x+80$
• $y^2=14 x^6+67 x^5+26 x^4+93 x^3+29 x^2+59 x+80$
• $y^2=4 x^6+30 x^5+5 x^4+67 x^3+81 x^2+89 x+83$
• $y^2=54 x^6+9 x^5+93 x^4+23 x^3+62 x^2+46 x+58$
• $y^2=32 x^6+62 x^5+82 x^4+85 x^3+52 x^2+66 x+64$
• $y^2=10 x^6+75 x^5+93 x^4+20 x^3+92 x^2+70 x+31$
• $y^2=8 x^6+84 x^5+67 x^4+77 x^3+36 x^2+14 x+41$
• $y^2=41 x^6+40 x^5+4 x^4+86 x^3+8 x^2+74 x+45$
• $y^2=17 x^6+25 x^5+11 x^4+10 x^3+17 x^2+83 x+15$

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 4.0.293725.1.

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.bh_rx	$2$	(not in LMFDB)