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

• Label: 2.97.aba_nr
• 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:	$1 - 26 x + 355 x^{2} - 2522 x^{3} + 9409 x^{4}$
Frobenius angles:	$\pm0.202933034032$, $\pm0.327277963104$
Angle rank:	$2$ (numerical)
Number field:	4.0.2503232.2
Galois group:	$D_{4}$
Jacobians:	$87$
Isomorphism classes:	87
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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$7217$	$88862921$	$835300545296$	$7839757122762761$	$73743341275862299377$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$72$	$9444$	$915222$	$88555524$	$8587448392$	$832971606654$	$80798277943560$	$7837433591669508$	$760231058882053206$	$73742412683635893604$

Jacobians and polarizations

This isogeny class is principally polarizable and contains the Jacobians of 87 curves (of which all are hyperelliptic):

• $y^2=20 x^6+13 x^5+58 x^4+20 x^3+58 x^2+67 x+95$
• $y^2=13 x^6+93 x^5+72 x^4+9 x^3+3 x^2+70 x+14$
• $y^2=19 x^6+75 x^5+57 x^4+49 x^3+57 x^2+72 x+26$
• $y^2=32 x^6+5 x^5+62 x^4+62 x^3+31 x^2+35 x+55$
• $y^2=74 x^6+30 x^5+2 x^4+39 x^3+96 x^2+10 x+87$
• $y^2=40 x^6+27 x^5+63 x^4+45 x^3+73 x^2+63 x+57$
• $y^2=83 x^6+25 x^5+58 x^4+22 x^3+57 x^2+38 x+1$
• $y^2=5 x^6+37 x^5+55 x^4+9 x^3+28 x^2+24 x+88$
• $y^2=13 x^6+2 x^5+47 x^4+x^3+21 x^2+21 x+96$
• $y^2=96 x^6+8 x^5+90 x^4+95 x^3+37 x^2+12 x+31$
• $y^2=70 x^6+21 x^5+x^4+2 x^3+58 x^2+71 x+24$
• $y^2=74 x^6+6 x^5+61 x^4+94 x^3+51 x^2+22 x+64$
• $y^2=25 x^6+73 x^5+51 x^4+85 x^3+58 x^2+85 x+68$
• $y^2=14 x^6+96 x^5+20 x^4+94 x^3+18 x^2+3 x+34$
• $y^2=34 x^6+43 x^5+45 x^4+18 x^3+32 x^2+67 x+55$
• $y^2=43 x^6+83 x^5+17 x^4+93 x^3+62 x^2+39 x+33$
• $y^2=13 x^6+18 x^5+9 x^4+85 x^3+58 x^2+13 x+64$
• $y^2=29 x^6+16 x^5+47 x^3+22 x^2+4 x+11$
• $y^2=63 x^6+64 x^5+26 x^4+39 x^3+23 x^2+14 x+10$
• $y^2=11 x^6+86 x^5+12 x^4+18 x^3+85 x^2+95$
• and

• $y^2=15 x^6+18 x^5+61 x^4+46 x^3+92 x^2+28 x+1$
• $y^2=13 x^6+84 x^5+40 x^4+75 x^3+81 x^2+65 x+46$
• $y^2=44 x^6+34 x^5+16 x^4+4 x^3+38 x^2+29 x+67$
• $y^2=85 x^6+4 x^5+8 x^4+44 x^3+94 x^2+50 x+65$
• $y^2=57 x^6+69 x^5+4 x^4+23 x^3+73 x^2+11 x+8$
• $y^2=47 x^6+39 x^5+74 x^4+37 x^3+71 x^2+86 x+26$
• $y^2=36 x^6+78 x^5+53 x^4+54 x^3+89 x^2+18 x+57$
• $y^2=21 x^6+63 x^5+73 x^4+58 x^3+23 x^2+77 x+39$
• $y^2=45 x^6+91 x^5+32 x^4+50 x^3+58 x^2+52 x+3$
• $y^2=33 x^6+8 x^5+66 x^4+2 x^3+69 x^2+10 x+34$
• $y^2=56 x^6+69 x^5+94 x^4+71 x^3+26 x^2+90 x+35$
• $y^2=35 x^6+4 x^5+75 x^4+54 x^3+5 x^2+48 x+50$
• $y^2=20 x^6+86 x^5+27 x^4+19 x^3+49 x^2+47 x+86$
• $y^2=41 x^6+30 x^5+58 x^4+84 x^3+59 x+48$
• $y^2=89 x^6+86 x^5+83 x^4+92 x^3+54 x^2+81 x+19$
• $y^2=96 x^6+20 x^5+12 x^4+95 x^3+53 x^2+40 x+9$
• $y^2=68 x^6+6 x^5+76 x^4+55 x^3+27 x^2+68 x+40$
• $y^2=19 x^6+63 x^5+3 x^4+18 x^3+11 x^2+85 x+69$
• $y^2=56 x^6+46 x^5+90 x^4+65 x^3+26 x^2+92 x+90$
• $y^2=93 x^6+20 x^5+83 x^4+76 x^3+77 x^2+38 x+38$
• $y^2=83 x^6+37 x^5+9 x^4+27 x^3+51 x^2+27 x+24$
• $y^2=15 x^6+92 x^5+4 x^4+25 x^3+51 x^2+42 x+74$
• $y^2=56 x^6+33 x^5+36 x^4+28 x^3+82 x^2+10 x+89$
• $y^2=48 x^6+47 x^5+4 x^4+90 x^3+22 x^2+19 x+76$
• $y^2=91 x^6+57 x^5+66 x^4+82 x^3+57 x^2+77 x+38$
• $y^2=69 x^6+50 x^5+45 x^4+95 x^3+80 x^2+10 x+72$
• $y^2=58 x^6+72 x^5+76 x^4+94 x^3+28 x^2+91 x+10$
• $y^2=44 x^6+54 x^5+33 x^4+11 x^3+76 x^2+92 x+64$
• $y^2=15 x^6+48 x^5+21 x^4+41 x^3+x^2+89 x+68$
• $y^2=33 x^6+x^5+62 x^4+60 x^3+10 x^2+23 x+90$
• $y^2=40 x^6+43 x^5+96 x^4+88 x^3+22 x^2+11 x+67$
• $y^2=83 x^6+26 x^5+56 x^4+54 x^3+29 x^2+47 x+73$
• $y^2=9 x^6+35 x^5+10 x^4+34 x^3+8 x^2+8 x+9$
• $y^2=10 x^6+33 x^5+60 x^4+29 x^3+46 x^2+57 x+14$
• $y^2=6 x^6+13 x^5+83 x^4+54 x^2+45 x+4$
• $y^2=83 x^6+58 x^5+8 x^4+80 x^3+34 x^2+2 x+43$
• $y^2=5 x^6+14 x^5+18 x^4+77 x^3+4 x^2+24 x+67$
• $y^2=51 x^6+35 x^5+50 x^4+14 x^3+24 x^2+50 x+93$
• $y^2=13 x^6+89 x^5+8 x^4+86 x^3+65 x^2+74 x+65$
• $y^2=37 x^6+30 x^5+62 x^4+31 x^3+24 x^2+21 x+9$
• $y^2=12 x^6+18 x^5+23 x^4+29 x^3+18 x^2+24 x+59$
• $y^2=34 x^6+41 x^5+9 x^4+34 x^3+15 x^2+46 x+57$
• $y^2=52 x^6+77 x^5+3 x^4+74 x^3+68 x^2+6 x+45$
• $y^2=21 x^6+42 x^5+88 x^4+71 x^3+76 x^2+9 x+93$
• $y^2=80 x^6+67 x^5+15 x^4+20 x^3+19 x^2+88 x+84$
• $y^2=9 x^6+8 x^5+70 x^4+87 x^3+57 x^2+38 x+53$
• $y^2=45 x^6+28 x^5+10 x^4+25 x^3+44 x^2+29 x+62$
• $y^2=2 x^6+47 x^5+47 x^4+85 x^3+62 x^2+3 x+29$
• $y^2=5 x^6+16 x^5+94 x^4+70 x^3+57 x^2+94 x+1$
• $y^2=3 x^6+4 x^5+35 x^4+51 x^3+28 x^2+22 x+52$
• $y^2=7 x^6+68 x^5+51 x^4+7 x^3+90 x^2+46 x+14$
• $y^2=89 x^6+42 x^5+59 x^4+53 x^3+92 x^2+89 x+78$
• $y^2=34 x^6+55 x^5+27 x^4+86 x^3+25 x^2+11 x+67$
• $y^2=38 x^6+77 x^5+13 x^4+78 x^3+92 x^2+90 x+28$
• $y^2=74 x^6+15 x^5+15 x^4+17 x^3+21 x^2+68 x+28$
• $y^2=83 x^6+82 x^5+13 x^4+15 x^3+7 x^2+86 x+43$
• $y^2=63 x^6+6 x^5+8 x^4+65 x^3+25 x^2+6 x+8$
• $y^2=85 x^6+59 x^5+76 x^4+25 x^3+60 x^2+88 x+20$
• $y^2=94 x^6+61 x^5+4 x^4+86 x^3+18 x^2+56 x+28$
• $y^2=59 x^6+34 x^5+33 x^4+16 x^3+56 x^2+38 x+29$
• $y^2=84 x^6+27 x^5+40 x^4+31 x^3+40 x^2+92 x+17$
• $y^2=6 x^6+7 x^5+73 x^4+40 x^3+4 x^2+84 x+59$
• $y^2=7 x^6+4 x^5+46 x^4+70 x^3+13 x^2+4 x+21$
• $y^2=77 x^6+95 x^5+74 x^4+94 x^3+63 x^2+37 x+57$
• $y^2=37 x^6+15 x^5+95 x^4+96 x^3+81 x^2+81 x+87$
• $y^2=59 x^6+71 x^5+68 x^4+22 x^3+48 x^2+74 x+22$
• $y^2=57 x^6+19 x^5+27 x^4+56 x^3+46 x^2+64 x+45$

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 4.0.2503232.2.

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.ba_nr	$2$	(not in LMFDB)