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

• Label: 2.97.al_im
• 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:	$1 - 11 x + 220 x^{2} - 1067 x^{3} + 9409 x^{4}$
Frobenius angles:	$\pm0.374587737883$, $\pm0.444149471859$
Angle rank:	$2$ (numerical)
Number field:	4.0.8991368.2
Galois group:	$D_{4}$
Jacobians:	$54$
Isomorphism classes:	54
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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$8552$	$91574816$	$835465302176$	$7836170191592576$	$73739722394589187752$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$87$	$9729$	$915402$	$88515009$	$8587026967$	$832971608094$	$80798308139895$	$7837433741973633$	$760231057596867786$	$73742412674367836929$

Jacobians and polarizations

This isogeny class is principally polarizable and contains the Jacobians of 54 curves (of which all are hyperelliptic):

• $y^2=32 x^6+79 x^5+69 x^4+8 x^3+65 x^2+77 x+60$
• $y^2=8 x^6+57 x^5+x^4+50 x^3+90 x^2+88 x+52$
• $y^2=84 x^6+13 x^5+36 x^4+79 x^3+49 x^2+42 x+58$
• $y^2=51 x^6+89 x^5+81 x^4+88 x^3+92 x^2+57 x+34$
• $y^2=47 x^6+89 x^5+63 x^4+53 x^3+74 x^2+11 x+51$
• $y^2=11 x^6+34 x^5+79 x^4+52 x^3+11 x^2+72 x+50$
• $y^2=8 x^6+21 x^5+46 x^4+63 x^3+27 x^2+53 x+51$
• $y^2=21 x^6+58 x^5+28 x^4+7 x^3+77 x^2+71 x+61$
• $y^2=67 x^6+34 x^5+10 x^4+60 x^3+29 x^2+64 x+68$
• $y^2=70 x^6+9 x^5+45 x^4+68 x^3+9 x^2+33 x+63$
• $y^2=59 x^6+73 x^5+39 x^4+68 x^3+29 x^2+73 x+58$
• $y^2=39 x^6+26 x^5+53 x^4+85 x^3+67 x+83$
• $y^2=13 x^6+4 x^5+60 x^4+49 x^3+85 x^2+43 x+71$
• $y^2=80 x^6+33 x^5+78 x^4+16 x^3+34 x^2+17 x+19$
• $y^2=26 x^6+23 x^5+89 x^4+15 x^3+59 x^2+77 x+33$
• $y^2=82 x^6+68 x^5+58 x^4+54 x^3+x^2+17 x+17$
• $y^2=21 x^6+92 x^5+81 x^4+66 x^3+83 x^2+51 x+86$
• $y^2=55 x^6+9 x^5+14 x^4+74 x^3+28 x^2+50 x+74$
• $y^2=42 x^6+27 x^5+54 x^4+28 x^3+42 x^2+16 x+35$
• $y^2=95 x^6+52 x^5+38 x^4+73 x^3+78 x^2+44 x+63$
• and

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

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 4.0.8991368.2.

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.l_im	$2$	(not in LMFDB)