Abelian variety isogeny class 2.113.au_il over $\F_{113}$

• Label: 2.113.au_il
• Base field: $\F_{113}$
• 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:	$\F_{113}$
Dimension:	$2$
L-polynomial:	$1 - 20 x + 219 x^{2} - 2260 x^{3} + 12769 x^{4}$
Frobenius angles:	$\pm0.0937886839908$, $\pm0.505151810104$
Angle rank:	$2$ (numerical)
Number field:	4.0.3155344400.1
Galois group:	$D_{4}$
Jacobians:	$80$
Isomorphism classes:	80

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$10709$	$163515721$	$2079588463316$	$26578695736604921$	$339456656118907619389$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$94$	$12808$	$1441258$	$163012116$	$18424347294$	$2081955189862$	$235260559060558$	$26584441836507108$	$3004041941546326954$	$339456739064738819928$

Jacobians and polarizations

This isogeny class is principally polarizable and contains the Jacobians of 80 curves (of which all are hyperelliptic):

• $y^2=22 x^6+45 x^5+82 x^4+90 x^3+36 x^2+22 x+111$
• $y^2=24 x^6+66 x^5+37 x^4+76 x^3+14 x^2+14 x+35$
• $y^2=60 x^6+99 x^5+99 x^4+19 x^3+103 x^2+52 x+44$
• $y^2=69 x^6+49 x^5+105 x^4+45 x^3+5 x^2+105 x+37$
• $y^2=102 x^6+7 x^5+108 x^4+31 x^3+97 x^2+6 x+19$
• $y^2=111 x^6+54 x^5+54 x^4+34 x^3+105 x^2+86 x+74$
• $y^2=54 x^6+82 x^5+111 x^4+16 x^3+89 x^2+44 x+10$
• $y^2=28 x^6+7 x^5+8 x^4+110 x^3+86 x^2+33 x+83$
• $y^2=30 x^6+66 x^5+64 x^4+28 x^3+108 x^2+32 x+35$
• $y^2=97 x^6+46 x^5+53 x^4+79 x^3+27 x^2+65 x+23$
• $y^2=74 x^6+19 x^5+6 x^4+72 x^2+102 x+35$
• $y^2=3 x^6+53 x^5+90 x^4+50 x^3+62 x^2+51 x+49$
• $y^2=59 x^6+27 x^5+108 x^4+61 x^3+74 x^2+30 x+90$
• $y^2=34 x^6+25 x^5+37 x^4+52 x^3+48 x^2+49 x+59$
• $y^2=93 x^6+100 x^5+109 x^4+37 x^3+61 x^2+67 x+63$
• $y^2=73 x^6+101 x^5+93 x^4+12 x^3+x^2+99 x+93$
• $y^2=88 x^6+111 x^5+84 x^4+15 x^3+42 x^2+106 x+54$
• $y^2=20 x^6+39 x^5+92 x^4+90 x^3+101 x^2+85 x+57$
• $y^2=90 x^6+18 x^5+85 x^4+40 x^3+44 x^2+108 x+54$
• $y^2=80 x^6+93 x^5+84 x^4+98 x^3+39 x^2+51 x+81$
• and

• $y^2=97 x^6+111 x^5+28 x^4+111 x^3+33 x^2+50 x+55$
• $y^2=46 x^6+9 x^5+106 x^4+55 x^3+13 x^2+27 x+71$
• $y^2=26 x^6+64 x^5+81 x^4+20 x^3+50 x^2+8 x+1$
• $y^2=79 x^6+89 x^5+59 x^4+68 x^2+28 x+67$
• $y^2=39 x^6+80 x^5+29 x^4+38 x^3+4 x^2+77 x+80$
• $y^2=x^6+68 x^5+100 x^4+53 x^3+16 x^2+44 x+9$
• $y^2=13 x^6+96 x^5+63 x^4+94 x^3+72 x^2+26 x+51$
• $y^2=64 x^6+22 x^5+63 x^4+44 x^3+6 x^2+42 x+14$
• $y^2=95 x^6+97 x^5+105 x^4+26 x^3+57 x^2+7 x+72$
• $y^2=98 x^6+48 x^5+106 x^4+19 x^3+x^2+36 x+12$
• $y^2=6 x^6+40 x^5+56 x^4+72 x^3+58 x^2+10 x+73$
• $y^2=25 x^6+40 x^5+81 x^4+23 x^3+86 x^2+86 x+85$
• $y^2=73 x^6+72 x^5+27 x^4+87 x^3+106 x^2+100 x+65$
• $y^2=8 x^6+110 x^5+100 x^4+92 x^3+5 x^2+62 x+50$
• $y^2=51 x^6+8 x^5+82 x^4+24 x^3+111 x^2+35 x+88$
• $y^2=36 x^6+82 x^5+22 x^4+94 x^3+38 x^2+62 x+44$
• $y^2=36 x^6+44 x^5+66 x^4+86 x^3+45 x^2+103 x+59$
• $y^2=42 x^6+74 x^5+93 x^4+107 x^3+24 x^2+58 x+92$
• $y^2=86 x^6+69 x^5+48 x^4+93 x^3+99 x^2+61 x+55$
• $y^2=95 x^6+52 x^5+61 x^4+83 x^3+87 x^2+80 x+92$
• $y^2=30 x^6+97 x^5+64 x^4+7 x^3+50 x^2+102 x+76$
• $y^2=105 x^6+9 x^5+38 x^4+48 x^3+107 x^2+46 x+89$
• $y^2=69 x^6+11 x^4+57 x^3+43 x^2+91 x+10$
• $y^2=76 x^6+37 x^5+97 x^4+52 x^3+94 x^2+90 x+10$
• $y^2=94 x^6+77 x^5+2 x^4+71 x^3+112 x^2+11 x+87$
• $y^2=36 x^6+33 x^5+106 x^4+73 x^3+57 x^2+48 x+38$
• $y^2=8 x^6+30 x^5+85 x^4+81 x^3+80 x^2+19 x+71$
• $y^2=96 x^6+33 x^5+14 x^4+29 x^3+34 x^2+29 x+36$
• $y^2=111 x^6+84 x^4+35 x^3+83 x^2+86 x+70$
• $y^2=106 x^6+22 x^5+46 x^4+27 x^3+29 x^2+69 x+83$
• $y^2=27 x^6+27 x^5+75 x^4+47 x^3+5 x^2+45 x+28$
• $y^2=5 x^6+72 x^5+14 x^4+111 x^3+53 x^2+106 x+89$
• $y^2=20 x^6+21 x^4+7 x^3+59 x^2+69 x+103$
• $y^2=47 x^6+24 x^5+64 x^4+70 x^3+87 x^2+101 x+9$
• $y^2=93 x^6+37 x^5+81 x^4+23 x^3+41 x^2+18 x+52$
• $y^2=80 x^6+95 x^5+72 x^4+71 x^3+101 x^2+59 x+86$
• $y^2=67 x^6+61 x^5+38 x^4+103 x^3+18 x^2+34 x+67$
• $y^2=48 x^6+45 x^5+101 x^4+70 x^3+6 x^2+62 x+102$
• $y^2=44 x^6+4 x^5+22 x^4+53 x^3+98 x^2+27 x+41$
• $y^2=29 x^6+71 x^5+16 x^4+63 x^3+91 x^2+89 x+25$
• $y^2=35 x^6+73 x^5+27 x^4+7 x^3+4 x^2+104 x+88$
• $y^2=46 x^6+67 x^5+41 x^4+93 x^3+110 x^2+43 x+28$
• $y^2=101 x^6+82 x^5+78 x^4+106 x^3+35 x^2+74 x+31$
• $y^2=71 x^6+78 x^5+40 x^4+97 x^3+20 x^2+98 x+94$
• $y^2=23 x^6+20 x^5+90 x^4+32 x^3+34 x^2+19 x+26$
• $y^2=x^6+95 x^5+24 x^4+42 x^3+30 x^2+73 x+45$
• $y^2=48 x^6+5 x^5+6 x^4+27 x^3+59 x^2+48 x+43$
• $y^2=86 x^6+55 x^5+80 x^4+98 x^3+56 x^2+99 x+78$
• $y^2=12 x^6+79 x^5+82 x^4+99 x^3+77 x^2+65 x+66$
• $y^2=63 x^6+66 x^5+81 x^4+80 x^3+74 x^2+90 x+78$
• $y^2=65 x^6+73 x^5+79 x^4+59 x^3+42 x^2+63 x+33$
• $y^2=64 x^6+56 x^5+74 x^4+71 x^3+46 x^2+103 x+1$
• $y^2=92 x^6+83 x^5+39 x^4+84 x^3+71 x^2+6 x+18$
• $y^2=35 x^6+78 x^5+104 x^4+31 x^3+74 x^2+96 x+5$
• $y^2=27 x^6+76 x^5+79 x^4+103 x^3+95 x^2+54 x+71$
• $y^2=51 x^6+96 x^5+106 x^4+51 x^3+53 x^2+83 x+46$
• $y^2=23 x^6+32 x^5+42 x^4+61 x^3+106 x^2+21 x+99$
• $y^2=71 x^6+89 x^5+37 x^4+22 x^3+102 x^2+106 x+67$
• $y^2=14 x^6+65 x^5+109 x^4+74 x^3+15 x^2+109 x+12$
• $y^2=45 x^6+88 x^5+20 x^4+39 x^3+76 x^2+56 x+74$

Decomposition and endomorphism algebra

All geometric endomorphisms are defined over $\F_{113}$.

Endomorphism algebra over $\F_{113}$

The endomorphism algebra of this simple isogeny class is 4.0.3155344400.1.

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
2.113.u_il	$2$	(not in LMFDB)