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

• Label: 2.97.h_go
• 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:	$1 + 7 x + 170 x^{2} + 679 x^{3} + 9409 x^{4}$
Frobenius angles:	$\pm0.459152563654$, $\pm0.660578414015$
Angle rank:	$2$ (numerical)
Number field:	4.0.2386001100.1
Galois group:	$D_{4}$
Jacobians:	$88$
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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$10266$	$91305804$	$831886379496$	$7836702651783936$	$73742383901383444986$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$105$	$9701$	$911484$	$88521025$	$8587336905$	$832971502082$	$80798305371273$	$7837433613575809$	$760231055341318428$	$73742412699966591461$

Jacobians and polarizations

This isogeny class is principally polarizable and contains the Jacobians of 88 curves (of which all are hyperelliptic):

• $y^2=30 x^6+30 x^5+67 x^4+65 x^3+2 x^2+8 x+45$
• $y^2=33 x^6+79 x^5+76 x^4+28 x^3+5 x^2+85 x+57$
• $y^2=80 x^6+17 x^5+25 x^4+88 x^3+32 x^2+9 x+40$
• $y^2=43 x^6+10 x^5+72 x^4+62 x^3+58 x^2+x+52$
• $y^2=63 x^6+x^5+11 x^4+38 x^3+31 x^2+61 x+8$
• $y^2=22 x^6+5 x^5+94 x^4+89 x^3+16 x^2+74 x+62$
• $y^2=58 x^6+32 x^5+29 x^4+27 x^3+14 x^2+66 x+93$
• $y^2=94 x^6+81 x^5+5 x^4+50 x^3+60 x^2+89 x+62$
• $y^2=61 x^6+74 x^5+50 x^4+92 x^3+38 x^2+85 x+84$
• $y^2=70 x^6+75 x^5+47 x^4+67 x^3+25 x^2+53 x+48$
• $y^2=30 x^6+56 x^5+58 x^4+62 x^3+63 x^2+83 x+66$
• $y^2=4 x^6+19 x^5+11 x^4+96 x^3+20 x^2+53 x+14$
• $y^2=12 x^6+49 x^5+29 x^4+17 x^3+24 x^2+55 x+27$
• $y^2=87 x^6+84 x^5+80 x^4+78 x^3+59 x^2+60 x+93$
• $y^2=63 x^6+27 x^5+66 x^4+60 x^3+10 x^2+78 x+66$
• $y^2=49 x^6+42 x^5+82 x^4+x^3+26 x^2+6 x+96$
• $y^2=8 x^6+85 x^5+73 x^4+34 x^3+63 x^2+96 x+60$
• $y^2=28 x^6+58 x^5+26 x^4+33 x^3+47 x^2+84 x+46$
• $y^2=86 x^6+12 x^5+4 x^4+95 x^3+93 x^2+59 x+25$
• $y^2=82 x^6+11 x^5+33 x^4+38 x^3+21 x^2+72 x+86$
• and

• $y^2=x^6+22 x^5+22 x^4+48 x^3+89 x^2+74 x+4$
• $y^2=4 x^6+80 x^5+51 x^4+14 x^3+35 x^2+30 x+96$
• $y^2=32 x^6+37 x^3+36 x^2+37 x+34$
• $y^2=95 x^6+50 x^5+94 x^4+51 x^3+55 x^2+80 x+93$
• $y^2=95 x^6+13 x^5+13 x^4+56 x^3+4 x^2+11 x+68$
• $y^2=34 x^6+52 x^5+83 x^4+38 x^3+22 x^2+11 x+75$
• $y^2=51 x^6+65 x^5+21 x^4+53 x^3+7 x^2+x+26$
• $y^2=94 x^6+15 x^5+65 x^4+12 x^3+31 x^2+45 x+6$
• $y^2=39 x^6+24 x^5+51 x^4+80 x^3+57 x^2+64 x+95$
• $y^2=65 x^6+92 x^5+95 x^4+75 x^3+28 x^2+71 x+26$
• $y^2=18 x^6+24 x^5+84 x^4+22 x^3+6 x^2+45 x+67$
• $y^2=68 x^6+40 x^5+67 x^4+43 x^3+50 x^2+89$
• $y^2=77 x^6+45 x^5+82 x^4+84 x^3+10 x^2+69 x+29$
• $y^2=76 x^6+79 x^5+41 x^4+59 x^3+28 x^2+62 x+39$
• $y^2=24 x^6+91 x^5+16 x^4+37 x^3+69 x^2+31 x+71$
• $y^2=62 x^6+32 x^5+59 x^4+24 x^3+31 x^2+45 x+49$
• $y^2=54 x^6+16 x^5+9 x^4+26 x^3+54 x^2+87 x+86$
• $y^2=61 x^6+13 x^5+23 x^4+12 x^3+47 x^2+86 x+60$
• $y^2=53 x^6+30 x^5+81 x^4+2 x^3+25 x^2+21 x+2$
• $y^2=81 x^6+7 x^5+71 x^4+88 x^3+31 x^2+38 x+88$
• $y^2=59 x^6+24 x^5+4 x^4+18 x^3+61 x^2+82 x+82$
• $y^2=81 x^6+78 x^5+94 x^4+32 x^3+58 x+61$
• $y^2=46 x^6+4 x^5+23 x^4+48 x^3+74 x^2+66 x+66$
• $y^2=88 x^6+14 x^5+30 x^4+2 x^3+79 x^2+12 x+89$
• $y^2=50 x^6+32 x^5+35 x^4+82 x^3+33 x^2+90 x+63$
• $y^2=88 x^6+18 x^5+45 x^4+38 x^3+6 x^2+21 x+91$
• $y^2=14 x^6+24 x^5+62 x^4+96 x^3+42 x^2+95 x+31$
• $y^2=34 x^6+42 x^5+31 x^4+92 x^3+61 x^2+36 x+71$
• $y^2=22 x^6+61 x^5+x^4+43 x^3+21 x^2+25 x+53$
• $y^2=33 x^6+78 x^5+75 x^4+3 x^3+43 x^2+50 x+59$
• $y^2=95 x^6+61 x^5+38 x^4+57 x^3+77 x^2+47 x+49$
• $y^2=9 x^6+82 x^5+32 x^4+11 x^3+33 x^2+85 x+54$
• $y^2=96 x^6+93 x^5+11 x^4+24 x^3+57 x^2+79 x+89$
• $y^2=4 x^6+40 x^5+81 x^4+90 x^3+73 x^2+91 x+23$
• $y^2=96 x^6+58 x^5+38 x^4+42 x^3+39 x^2+2 x$
• $y^2=54 x^6+46 x^5+64 x^4+78 x^3+3 x^2+21 x+40$
• $y^2=26 x^6+34 x^5+4 x^3+55 x^2+67 x+37$
• $y^2=39 x^6+37 x^5+45 x^4+3 x^3+4 x^2+93 x+43$
• $y^2=72 x^6+52 x^5+11 x^4+59 x^3+90 x^2+58 x+16$
• $y^2=46 x^6+13 x^5+79 x^4+47 x^3+94 x^2+46 x+47$
• $y^2=71 x^6+87 x^5+81 x^4+75 x^3+88 x^2+29 x+41$
• $y^2=16 x^6+22 x^5+84 x^4+51 x^3+94 x^2+68 x+21$
• $y^2=90 x^6+75 x^5+20 x^4+89 x^3+45 x^2+71 x+13$
• $y^2=26 x^6+31 x^5+59 x^4+35 x^3+32 x^2+16 x+21$
• $y^2=76 x^6+35 x^5+74 x^4+x^3+85 x^2+85 x+79$
• $y^2=32 x^6+38 x^5+38 x^4+73 x^3+94 x^2+27 x+47$
• $y^2=73 x^6+45 x^5+55 x^4+8 x^3+20 x^2+20 x+25$
• $y^2=83 x^6+60 x^5+41 x^4+15 x^3+14 x^2+70 x+38$
• $y^2=31 x^6+60 x^4+63 x^3+91 x^2+81 x+76$
• $y^2=12 x^6+12 x^5+9 x^4+10 x^3+61 x^2+65 x+25$
• $y^2=48 x^6+70 x^5+79 x^4+25 x^3+44 x^2+23 x+45$
• $y^2=73 x^6+6 x^5+50 x^4+17 x^3+50 x^2+66 x+51$
• $y^2=22 x^6+4 x^5+38 x^4+10 x^3+29 x^2+84 x+29$
• $y^2=54 x^6+23 x^5+16 x^4+4 x^3+4 x^2+22 x+58$
• $y^2=5 x^6+29 x^5+41 x^4+7 x^3+30 x^2+34 x+41$
• $y^2=73 x^6+4 x^5+19 x^4+62 x^3+9 x^2+3 x+67$
• $y^2=12 x^6+86 x^5+83 x^4+33 x^3+27 x^2+58 x+40$
• $y^2=37 x^6+7 x^5+7 x^4+95 x^3+21 x^2+44 x+89$
• $y^2=76 x^6+30 x^5+76 x^4+2 x^3+2 x^2+42 x+79$
• $y^2=62 x^6+34 x^5+44 x^4+42 x^3+14 x^2+44 x+73$
• $y^2=21 x^6+x^5+63 x^4+56 x^3+31 x^2+93 x+8$
• $y^2=70 x^6+56 x^5+15 x^4+24 x^3+20 x^2+x+54$
• $y^2=31 x^6+67 x^5+95 x^4+80 x^3+79 x^2+85 x+67$
• $y^2=5 x^6+42 x^5+37 x^4+42 x^3+57 x^2+3$
• $y^2=24 x^6+3 x^5+12 x^3+75 x^2+42$
• $y^2=82 x^6+84 x^5+24 x^4+6 x^3+81 x^2+67 x+31$
• $y^2=41 x^6+20 x^5+18 x^4+32 x^3+8 x^2+20 x+77$
• $y^2=61 x^6+25 x^5+80 x^4+5 x^3+41 x^2+25 x+83$

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 4.0.2386001100.1.

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.ah_go	$2$	(not in LMFDB)