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

• Label: 2.97.abb_oi
• 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:	$1 - 27 x + 372 x^{2} - 2619 x^{3} + 9409 x^{4}$
Frobenius angles:	$\pm0.210071069217$, $\pm0.302779256252$
Angle rank:	$2$ (numerical)
Number field:	4.0.677416.1
Galois group:	$D_{4}$
Jacobians:	$56$
Cyclic group of points:	no
Non-cyclic primes:	$2$

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$7136$	$88686208$	$835340873600$	$7840207372900864$	$73743914914380483296$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$71$	$9425$	$915266$	$88560609$	$8587515191$	$832971721790$	$80798269415543$	$7837433456409409$	$760231058145229442$	$73742412690279880625$

Jacobians and polarizations

This isogeny class is principally polarizable and contains the Jacobians of 56 curves (of which all are hyperelliptic):

• $y^2=83 x^6+3 x^4+86 x^3+81 x^2+72 x+28$
• $y^2=6 x^6+77 x^5+63 x^4+6 x^3+79 x^2+94 x+90$
• $y^2=37 x^6+31 x^5+90 x^4+33 x^3+74 x^2+56 x+40$
• $y^2=92 x^6+14 x^5+50 x^4+75 x^3+19 x^2+63 x+93$
• $y^2=74 x^6+42 x^5+70 x^4+77 x^3+42 x^2+18 x+7$
• $y^2=82 x^6+53 x^5+72 x^4+58 x^3+11 x^2+22 x+58$
• $y^2=34 x^6+39 x^5+63 x^4+51 x^3+25 x^2+31 x+29$
• $y^2=5 x^6+79 x^5+37 x^4+27 x^3+29 x^2+7 x+68$
• $y^2=80 x^6+10 x^5+49 x^4+74 x^3+76 x^2+84 x+4$
• $y^2=45 x^6+49 x^5+14 x^4+11 x^3+34 x^2+20 x+38$
• $y^2=60 x^6+48 x^5+63 x^4+79 x^3+14 x^2+4 x+68$
• $y^2=5 x^6+82 x^5+35 x^4+33 x^3+40 x^2+47$
• $y^2=19 x^6+29 x^5+63 x^4+54 x^3+56 x^2+31 x+3$
• $y^2=96 x^6+50 x^5+74 x^4+96 x^3+54 x^2+66 x+90$
• $y^2=44 x^6+77 x^5+90 x^4+55 x^3+82 x^2+55 x+42$
• $y^2=77 x^6+22 x^5+47 x^4+8 x^3+63 x^2+9 x+25$
• $y^2=37 x^6+22 x^5+82 x^4+45 x^3+56 x^2+58 x+34$
• $y^2=17 x^6+65 x^5+87 x^4+38 x^3+40 x^2+66 x+30$
• $y^2=45 x^5+60 x^4+60 x^3+45 x^2+67 x+24$
• $y^2=34 x^6+93 x^5+6 x^4+92 x^3+10 x^2+31 x+92$
• and

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

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 4.0.677416.1.

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.bb_oi	$2$	(not in LMFDB)