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

• Label: 2.97.x_ln
• 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:	$1 + 23 x + 299 x^{2} + 2231 x^{3} + 9409 x^{4}$
Frobenius angles:	$\pm0.603283496309$, $\pm0.822696768988$
Angle rank:	$2$ (numerical)
Number field:	4.0.449066157.1
Galois group:	$D_{4}$
Jacobians:	$100$
Isomorphism classes:	100
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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$11963$	$89184165$	$831357786707$	$7838002513761525$	$73742510638898602928$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$121$	$9479$	$910903$	$88535707$	$8587351666$	$832973123351$	$80798257672603$	$7837433790591763$	$760231059553937461$	$73742412659418910814$

Jacobians and polarizations

This isogeny class is principally polarizable and contains the Jacobians of 100 curves (of which all are hyperelliptic):

• $y^2=22 x^6+85 x^5+64 x^4+92 x^3+67 x^2+4 x+38$
• $y^2=68 x^6+78 x^5+80 x^4+62 x^3+56 x^2+2 x+48$
• $y^2=25 x^6+44 x^5+12 x^4+79 x^3+80 x^2+26 x+72$
• $y^2=18 x^6+36 x^5+37 x^4+50 x^3+11 x^2+22 x+40$
• $y^2=x^6+45 x^5+22 x^4+80 x^3+48 x^2+75 x+9$
• $y^2=33 x^6+29 x^5+79 x^4+64 x^3+71 x^2+89 x+27$
• $y^2=24 x^6+77 x^5+84 x^4+70 x^3+64 x^2+69 x+76$
• $y^2=30 x^6+29 x^5+27 x^4+54 x^3+10 x^2+50 x+54$
• $y^2=8 x^6+9 x^5+4 x^4+85 x^3+53 x^2+66 x+92$
• $y^2=34 x^6+21 x^5+21 x^4+50 x^3+86 x^2+18 x+47$
• $y^2=16 x^6+33 x^5+35 x^4+8 x^3+41 x^2+30 x+4$
• $y^2=35 x^6+79 x^5+33 x^4+67 x^3+40 x^2+91 x$
• $y^2=41 x^6+74 x^5+56 x^4+5 x^3+28 x^2+77 x+2$
• $y^2=53 x^6+4 x^5+19 x^4+60 x^3+14 x^2+30 x+12$
• $y^2=5 x^6+61 x^5+51 x^4+81 x^3+19 x^2+7 x+10$
• $y^2=44 x^6+77 x^5+74 x^4+2 x^3+3 x^2+88 x+39$
• $y^2=3 x^6+50 x^5+28 x^4+37 x^3+75 x^2+20 x+61$
• $y^2=67 x^6+2 x^5+77 x^4+82 x^3+86 x^2+64 x+53$
• $y^2=49 x^6+84 x^5+78 x^4+35 x^3+80 x^2+70 x+54$
• $y^2=51 x^6+49 x^5+74 x^4+63 x^3+23 x^2+49 x+89$
• and

• $y^2=60 x^6+96 x^5+60 x^4+34 x^3+87 x^2+64 x+4$
• $y^2=79 x^6+52 x^5+28 x^4+12 x^3+68 x^2+34 x+93$
• $y^2=23 x^6+13 x^5+34 x^4+37 x^3+55 x^2+12 x+45$
• $y^2=36 x^6+75 x^5+69 x^4+92 x^3+85 x^2+38 x+94$
• $y^2=27 x^6+28 x^5+93 x^4+18 x^3+25 x^2+9 x+84$
• $y^2=47 x^6+88 x^5+7 x^4+6 x^3+19 x^2+6 x+1$
• $y^2=50 x^6+88 x^5+95 x^4+79 x^3+92 x^2+54 x+11$
• $y^2=3 x^6+79 x^5+53 x^4+75 x^3+7 x^2+47 x+36$
• $y^2=24 x^6+81 x^5+55 x^4+47 x^3+49 x^2+6 x+61$
• $y^2=27 x^6+20 x^5+61 x^4+21 x^3+84 x^2+60 x+23$
• $y^2=x^6+6 x^5+18 x^4+74 x^3+15 x^2+56 x+6$
• $y^2=85 x^6+9 x^5+40 x^4+29 x^3+12 x^2+25 x+4$
• $y^2=33 x^6+79 x^5+19 x^4+42 x^3+14 x^2+x+68$
• $y^2=95 x^6+53 x^5+73 x^4+59 x^3+38 x^2+23 x+35$
• $y^2=73 x^6+67 x^5+30 x^4+45 x^3+57 x^2+5 x+66$
• $y^2=19 x^6+74 x^5+37 x^4+14 x^3+20 x^2+64 x+8$
• $y^2=72 x^6+13 x^5+28 x^4+19 x^3+77 x^2+41 x+71$
• $y^2=2 x^6+89 x^5+33 x^4+51 x^3+68 x^2+30 x+49$
• $y^2=91 x^6+25 x^5+95 x^4+49 x^3+40 x^2+50 x+12$
• $y^2=12 x^6+57 x^5+49 x^4+8 x^3+53 x^2+86 x+32$
• $y^2=16 x^6+36 x^5+92 x^4+68 x^3+43 x^2+6 x+9$
• $y^2=85 x^6+70 x^5+32 x^4+34 x^3+43 x^2+91$
• $y^2=57 x^6+3 x^5+46 x^4+15 x^3+22 x^2+9 x+63$
• $y^2=43 x^6+59 x^5+11 x^4+2 x^3+72 x^2+24 x+8$
• $y^2=29 x^6+36 x^5+22 x^4+9 x^3+53 x^2+63 x+93$
• $y^2=47 x^6+78 x^5+47 x^4+74 x^3+30 x^2+40 x+37$
• $y^2=28 x^6+56 x^5+4 x^4+46 x^3+51 x^2+95 x+48$
• $y^2=45 x^6+78 x^5+24 x^4+41 x^3+73 x^2+52 x+90$
• $y^2=4 x^6+9 x^5+7 x^4+80 x^3+51 x^2+87 x+88$
• $y^2=36 x^6+79 x^5+2 x^4+67 x^3+38 x^2+92 x+30$
• $y^2=15 x^6+90 x^5+75 x^4+43 x^3+31 x^2+95 x+60$
• $y^2=10 x^6+23 x^5+76 x^4+42 x^3+73 x^2+50 x+43$
• $y^2=50 x^6+66 x^5+6 x^4+14 x^3+7 x^2+77 x+30$
• $y^2=60 x^6+45 x^5+52 x^4+41 x^3+50 x^2+84 x+49$
• $y^2=86 x^6+59 x^5+78 x^4+57 x^3+59 x^2+61 x+42$
• $y^2=31 x^6+30 x^5+34 x^4+29 x^3+53 x^2+86 x+91$
• $y^2=32 x^6+6 x^5+96 x^4+63 x^3+19 x^2+80 x+44$
• $y^2=65 x^6+85 x^5+26 x^4+53 x^3+64 x^2+90 x+11$
• $y^2=86 x^6+43 x^5+21 x^4+41 x^3+8 x^2+79 x+6$
• $y^2=12 x^6+13 x^5+x^4+63 x^3+68 x^2+32 x+60$
• $y^2=76 x^6+75 x^5+57 x^4+68 x^3+25 x^2+40 x+84$
• $y^2=47 x^6+63 x^5+78 x^4+12 x^3+35 x^2+58 x+91$
• $y^2=7 x^6+41 x^5+66 x^4+85 x^3+74 x^2+43 x+64$
• $y^2=51 x^6+91 x^5+43 x^4+14 x^3+38 x^2+95 x+50$
• $y^2=30 x^6+57 x^5+18 x^4+94 x^3+63 x^2+14 x$
• $y^2=19 x^6+58 x^5+64 x^4+57 x^3+90 x^2+37 x+96$
• $y^2=61 x^6+48 x^5+24 x^4+9 x^3+62 x^2+72 x+37$
• $y^2=36 x^6+54 x^5+84 x^3+48 x^2+38 x+62$
• $y^2=54 x^6+38 x^5+68 x^4+14 x^3+18 x^2+38 x+51$
• $y^2=75 x^6+7 x^5+3 x^4+53 x^3+13 x^2+90 x+84$
• $y^2=35 x^6+34 x^5+71 x^4+72 x^3+71 x^2+6 x+63$
• $y^2=28 x^6+96 x^5+96 x^4+52 x^3+14 x^2+63 x$
• $y^2=70 x^6+13 x^5+6 x^4+65 x^3+38 x^2+x+80$
• $y^2=48 x^6+34 x^5+59 x^4+81 x^3+75 x^2+94 x+63$
• $y^2=65 x^6+91 x^5+64 x^4+30 x^3+92 x^2+8 x+42$
• $y^2=78 x^6+21 x^5+80 x^4+36 x^3+8 x^2+18 x+7$
• $y^2=17 x^6+69 x^5+51 x^4+87 x^3+44 x^2+82 x+79$
• $y^2=6 x^6+34 x^5+74 x^4+70 x^3+76 x^2+33 x+35$
• $y^2=34 x^6+70 x^5+23 x^4+87 x^3+84 x^2+77 x+53$
• $y^2=18 x^6+30 x^5+48 x^4+5 x^3+10 x^2+89 x+82$
• $y^2=11 x^6+45 x^5+75 x^4+21 x^3+57 x^2+42 x+34$
• $y^2=54 x^6+68 x^5+43 x^4+3 x^3+54 x^2+28 x+50$
• $y^2=8 x^6+5 x^5+62 x^4+76 x^3+72 x^2+4 x+48$
• $y^2=8 x^6+44 x^5+95 x^4+74 x^3+9 x^2+79 x+57$
• $y^2=24 x^6+7 x^5+10 x^4+7 x^3+32 x^2+44 x+24$
• $y^2=86 x^6+51 x^5+18 x^4+75 x^3+32 x^2+32 x$
• $y^2=44 x^6+27 x^5+24 x^4+19 x^3+70 x^2+29 x+67$
• $y^2=50 x^6+22 x^5+40 x^4+55 x^3+65 x^2+72 x+40$
• $y^2=19 x^6+28 x^5+40 x^3+20 x^2+68 x+32$
• $y^2=56 x^6+25 x^5+47 x^4+34 x^3+58 x^2+8 x+20$
• $y^2=14 x^6+51 x^5+31 x^4+79 x^3+85 x^2+80 x+77$
• $y^2=9 x^6+42 x^5+79 x^4+35 x^3+23 x^2+89 x+65$
• $y^2=75 x^6+22 x^5+61 x^4+36 x^3+15 x^2+79 x+4$
• $y^2=50 x^6+82 x^5+32 x^4+37 x^3+83 x^2+64 x+13$
• $y^2=91 x^6+11 x^5+38 x^4+81 x^3+85 x^2+96 x+62$
• $y^2=27 x^6+59 x^5+89 x^4+57 x^3+42 x^2+78 x+11$
• $y^2=15 x^6+81 x^5+94 x^4+94 x^3+9 x^2+80 x+47$
• $y^2=42 x^6+48 x^5+55 x^4+69 x^3+5 x^2+27 x+40$
• $y^2=26 x^6+41 x^5+18 x^4+61 x^3+3 x^2+29 x+32$
• $y^2=91 x^6+50 x^5+91 x^4+41 x^3+28 x^2+29 x$

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 4.0.449066157.1.

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_ln	$2$	(not in LMFDB)