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

• Label: 2.97.x_kf
• 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:	$1 + 23 x + 265 x^{2} + 2231 x^{3} + 9409 x^{4}$
Frobenius angles:	$\pm0.559716706495$, $\pm0.938083206592$
Angle rank:	$2$ (numerical)
Number field:	4.0.135725.1
Galois group:	$D_{4}$
Jacobians:	$42$
Cyclic group of points:	yes

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$11929$	$88525109$	$833496992281$	$7835028880910501$	$73744592429669645584$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$121$	$9411$	$913249$	$88502115$	$8587594086$	$832972073907$	$80798270826625$	$7837433579406339$	$760231060074378793$	$73742412690611796286$

Jacobians and polarizations

This isogeny class is principally polarizable and contains the Jacobians of 42 curves (of which all are hyperelliptic):

• $y^2=93 x^6+12 x^5+94 x^4+96 x^3+38 x^2+10 x+88$
• $y^2=61 x^5+39 x^4+84 x^3+4 x^2+59 x+93$
• $y^2=63 x^6+24 x^5+5 x^4+93 x^3+76 x^2+49 x+20$
• $y^2=12 x^6+93 x^5+35 x^4+25 x^3+67 x^2+51 x+20$
• $y^2=76 x^6+30 x^5+47 x^4+x^3+31 x^2+38 x+41$
• $y^2=32 x^6+50 x^5+48 x^4+43 x^3+76 x^2+33 x+18$
• $y^2=63 x^6+3 x^5+92 x^4+14 x^3+2 x^2+85 x+64$
• $y^2=36 x^6+17 x^5+29 x^4+78 x^3+94 x^2+70 x+29$
• $y^2=63 x^6+12 x^5+73 x^4+91 x^3+20 x^2+88 x+68$
• $y^2=79 x^6+37 x^5+53 x^4+9 x^3+72 x^2+63 x+31$
• $y^2=60 x^6+67 x^5+53 x^4+80 x^3+69 x^2+91 x+95$
• $y^2=82 x^6+78 x^5+32 x^4+19 x^3+89 x^2+71 x+61$
• $y^2=24 x^6+64 x^5+70 x^4+51 x^3+88 x^2+71 x+12$
• $y^2=56 x^6+71 x^5+42 x^4+47 x^3+23 x^2+67 x+86$
• $y^2=96 x^6+58 x^5+53 x^4+11 x^3+32 x^2+65 x+3$
• $y^2=30 x^6+88 x^5+93 x^4+x^3+8 x+75$
• $y^2=2 x^6+47 x^5+31 x^4+53 x^3+34 x^2+79 x+21$
• $y^2=85 x^6+19 x^5+72 x^4+85 x^3+16 x^2+96 x+78$
• $y^2=3 x^6+74 x^5+33 x^4+39 x^3+29 x^2+91 x+13$
• $y^2=62 x^6+2 x^5+82 x^4+63 x^3+70 x^2+96 x+81$
• and

• $y^2=48 x^6+69 x^5+80 x^4+61 x^3+96 x^2+6 x+71$
• $y^2=5 x^6+65 x^5+96 x^4+47 x^3+67 x^2+79 x+9$
• $y^2=72 x^6+71 x^5+74 x^4+46 x^3+42 x^2+36 x+73$
• $y^2=9 x^6+34 x^5+83 x^4+24 x^3+33 x^2+7 x+10$
• $y^2=3 x^6+63 x^5+56 x^3+37 x^2+49 x+89$
• $y^2=3 x^6+40 x^5+11 x^4+5 x^2+56 x+13$
• $y^2=71 x^6+93 x^5+75 x^4+72 x^3+39 x^2+53 x+80$
• $y^2=95 x^6+19 x^5+79 x^4+59 x^3+2 x^2+47 x+96$
• $y^2=73 x^6+81 x^5+90 x^4+37 x^3+23 x^2+40 x+8$
• $y^2=4 x^6+72 x^5+46 x^4+32 x^3+20 x^2+41 x+72$
• $y^2=62 x^6+55 x^5+75 x^4+27 x^3+91 x^2+31 x+83$
• $y^2=84 x^6+80 x^5+70 x^4+55 x^3+60 x^2+96 x+73$
• $y^2=22 x^6+37 x^5+95 x^4+81 x^3+63 x^2+30 x+54$
• $y^2=30 x^6+55 x^5+62 x^4+20 x^3+51 x^2+71 x+76$
• $y^2=69 x^6+89 x^5+19 x^4+86 x^3+23 x^2+57 x+10$
• $y^2=27 x^6+20 x^5+72 x^4+96 x^3+59 x^2+41 x+91$
• $y^2=2 x^6+73 x^5+93 x^4+32 x^3+76 x^2+56 x+75$
• $y^2=60 x^6+53 x^5+64 x^4+35 x^3+65 x^2+4 x+18$
• $y^2=31 x^6+91 x^5+40 x^4+35 x^3+21 x^2+73 x+62$
• $y^2=78 x^6+14 x^5+73 x^4+68 x^3+33 x^2+85 x+33$
• $y^2=66 x^6+16 x^5+69 x^4+45 x^3+19 x^2+82 x+96$
• $y^2=86 x^6+41 x^5+4 x^4+21 x^3+40 x^2+82 x+3$

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 4.0.135725.1.

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.ax_kf	$2$	(not in LMFDB)