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

• Label: 2.113.ay_my
• 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:	$1 - 24 x + 336 x^{2} - 2712 x^{3} + 12769 x^{4}$
Frobenius angles:	$\pm0.183317634869$, $\pm0.406288938197$
Angle rank:	$2$ (numerical)
Number field:	4.0.1026380032.1
Galois group:	$D_{4}$
Jacobians:	$96$

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$10370$	$164281540$	$2085175883810$	$26585632333738000$	$339456592595185882850$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$90$	$12866$	$1445130$	$163054662$	$18424343850$	$2081953936514$	$235260594424890$	$26584442193636478$	$3004041934774480410$	$339456738924187646786$

Jacobians and polarizations

This isogeny class is principally polarizable and contains the Jacobians of 96 curves (of which all are hyperelliptic):

• $y^2=85 x^6+83 x^5+87 x^4+22 x^3+98 x^2+15 x+8$
• $y^2=92 x^6+110 x^5+33 x^4+4 x^3+6 x^2+12 x+75$
• $y^2=33 x^6+107 x^5+57 x^4+91 x^3+100 x^2+48 x+84$
• $y^2=74 x^6+30 x^5+32 x^4+60 x^3+85 x^2+90 x+108$
• $y^2=65 x^6+53 x^5+54 x^4+92 x^3+60 x^2+14 x+69$
• $y^2=110 x^6+61 x^4+10 x^3+8 x^2+103 x+48$
• $y^2=18 x^6+110 x^5+99 x^4+27 x^3+74 x^2+104 x+1$
• $y^2=30 x^6+51 x^5+83 x^4+40 x^3+11 x^2+2 x+68$
• $y^2=13 x^6+11 x^5+23 x^4+90 x^3+109 x^2+28 x+97$
• $y^2=23 x^6+110 x^5+22 x^4+64 x^3+14 x^2+51 x+27$
• $y^2=91 x^6+104 x^5+90 x^4+90 x^3+19 x^2+17 x+56$
• $y^2=42 x^6+93 x^5+53 x^4+69 x^3+62 x^2+62 x+28$
• $y^2=4 x^6+42 x^5+3 x^4+55 x^3+110 x^2+61 x+65$
• $y^2=99 x^6+19 x^5+50 x^4+69 x^3+62 x^2+88 x+84$
• $y^2=15 x^6+105 x^5+44 x^4+35 x^3+110 x^2+47 x+59$
• $y^2=64 x^6+16 x^5+44 x^4+32 x^3+18 x^2+57 x+44$
• $y^2=2 x^6+106 x^5+96 x^4+6 x^3+78 x^2+91 x+90$
• $y^2=103 x^6+99 x^5+64 x^4+106 x^3+22 x^2+107 x+34$
• $y^2=46 x^6+48 x^5+40 x^4+44 x^3+32 x^2+16 x+22$
• $y^2=67 x^6+18 x^5+78 x^4+108 x^3+110 x^2+109 x+9$
• and

• $y^2=39 x^6+65 x^5+75 x^4+68 x^3+99 x^2+24 x+103$
• $y^2=35 x^6+34 x^5+101 x^4+93 x^3+78 x^2+96 x+70$
• $y^2=102 x^6+109 x^5+61 x^4+97 x^3+111 x^2+72 x+101$
• $y^2=43 x^6+71 x^5+106 x^4+82 x^3+37 x^2+48 x+104$
• $y^2=108 x^6+108 x^5+65 x^4+27 x^3+59 x^2+105 x+45$
• $y^2=85 x^6+11 x^5+80 x^4+89 x^2+99 x+65$
• $y^2=48 x^6+12 x^5+102 x^4+107 x^3+8 x^2+55 x+73$
• $y^2=46 x^6+60 x^5+55 x^4+51 x^3+19 x^2+8 x+29$
• $y^2=82 x^6+65 x^5+17 x^4+73 x^3+79 x^2+44 x+65$
• $y^2=65 x^6+75 x^5+66 x^4+84 x^3+96 x^2+19 x+107$
• $y^2=50 x^6+68 x^5+52 x^4+23 x^3+42 x^2+18 x+38$
• $y^2=75 x^6+57 x^5+104 x^4+83 x^3+25 x^2+71 x+34$
• $y^2=37 x^6+94 x^5+73 x^4+84 x^3+18 x^2+50 x+21$
• $y^2=79 x^6+10 x^5+41 x^4+39 x^3+x^2+24 x+38$
• $y^2=76 x^6+5 x^5+111 x^4+93 x^3+88 x^2+4 x+28$
• $y^2=5 x^6+83 x^5+80 x^4+52 x^3+111 x^2+72 x+17$
• $y^2=96 x^6+2 x^5+74 x^4+29 x^3+61 x^2+30 x+21$
• $y^2=58 x^6+50 x^5+39 x^4+108 x^3+25 x^2+20 x+68$
• $y^2=39 x^6+25 x^5+91 x^4+49 x^3+54 x^2+92 x+15$
• $y^2=109 x^6+52 x^5+76 x^4+22 x^3+5 x^2+2$
• $y^2=97 x^6+83 x^5+23 x^4+62 x^3+96 x^2+75 x+68$
• $y^2=31 x^6+15 x^5+66 x^4+17 x^3+38 x^2+31 x+90$
• $y^2=24 x^6+22 x^5+53 x^4+91 x^3+103 x^2+103 x+6$
• $y^2=24 x^6+105 x^5+73 x^4+29 x^3+35 x^2+108 x+25$
• $y^2=x^6+53 x^5+6 x^4+19 x^2+96 x+88$
• $y^2=25 x^6+68 x^5+71 x^4+76 x^3+60 x^2+39 x+107$
• $y^2=45 x^6+89 x^5+35 x^3+75 x^2+29 x+24$
• $y^2=75 x^6+37 x^5+68 x^4+74 x^3+39 x^2+24 x+42$
• $y^2=109 x^6+37 x^5+54 x^4+33 x^3+51 x^2+43 x+6$
• $y^2=21 x^6+101 x^5+95 x^4+58 x^3+22 x^2+14 x+55$
• $y^2=107 x^6+26 x^5+51 x^4+88 x^3+92 x^2+x+53$
• $y^2=94 x^6+10 x^5+99 x^4+41 x^3+53 x^2+76 x+11$
• $y^2=21 x^6+37 x^5+47 x^4+71 x^3+65 x^2+52 x+17$
• $y^2=65 x^6+74 x^5+70 x^4+20 x^3+61 x^2+62 x+27$
• $y^2=89 x^6+60 x^5+86 x^4+70 x^3+87 x^2+92 x+35$
• $y^2=85 x^6+66 x^5+111 x^4+86 x^3+44 x^2+59 x+71$
• $y^2=62 x^6+73 x^5+60 x^4+46 x^3+25 x^2+20 x+73$
• $y^2=108 x^6+46 x^5+41 x^4+100 x^3+20 x^2+100 x+87$
• $y^2=9 x^6+33 x^5+33 x^4+18 x^3+70 x^2+109 x+28$
• $y^2=89 x^6+9 x^5+7 x^4+12 x^3+23 x^2+90 x+34$
• $y^2=27 x^6+76 x^5+72 x^4+100 x^3+35 x^2+77 x+109$
• $y^2=67 x^6+66 x^5+97 x^4+51 x^3+7 x^2+54 x+37$
• $y^2=22 x^6+7 x^5+46 x^4+64 x^3+80 x^2+70 x+71$
• $y^2=10 x^6+3 x^5+80 x^4+5 x^3+12 x^2+110 x+92$
• $y^2=108 x^6+96 x^5+37 x^4+70 x^3+51 x^2+62 x+8$
• $y^2=x^6+72 x^5+87 x^4+56 x^3+18 x^2+25 x+66$
• $y^2=74 x^6+105 x^5+70 x^4+9 x^3+16 x^2+50 x+101$
• $y^2=19 x^6+51 x^5+22 x^4+87 x^3+58 x^2+59 x+34$
• $y^2=95 x^6+37 x^5+40 x^4+66 x^3+62 x^2+57 x+79$
• $y^2=92 x^6+83 x^5+105 x^4+49 x^3+45 x^2+105 x+86$
• $y^2=107 x^6+35 x^5+62 x^4+70 x^3+50 x^2+80 x+25$
• $y^2=49 x^6+45 x^5+50 x^4+35 x^3+62 x^2+60$
• $y^2=69 x^6+106 x^5+53 x^4+94 x^3+46 x^2+72 x+36$
• $y^2=56 x^6+5 x^5+5 x^4+48 x^3+21 x^2+18 x+31$
• $y^2=6 x^6+75 x^5+27 x^4+95 x^3+52 x^2+37 x+42$
• $y^2=46 x^6+74 x^5+111 x^4+24 x^3+29 x^2+x+96$
• $y^2=41 x^6+85 x^5+29 x^4+94 x^3+47 x^2+96 x+18$
• $y^2=45 x^6+24 x^5+110 x^4+78 x^3+77 x^2+112 x+25$
• $y^2=84 x^6+68 x^5+60 x^4+42 x^3+91 x^2+3 x+3$
• $y^2=65 x^6+7 x^5+107 x^4+47 x^3+91 x^2+98 x+24$
• $y^2=18 x^6+87 x^5+69 x^4+98 x^3+66 x^2+25 x+77$
• $y^2=31 x^6+32 x^5+97 x^4+10 x^3+67 x^2+29 x+56$
• $y^2=47 x^6+29 x^5+70 x^4+90 x^3+101 x^2+71 x+70$
• $y^2=5 x^6+44 x^5+15 x^4+40 x^3+57 x^2+19 x$
• $y^2=18 x^6+89 x^5+68 x^4+39 x^3+83 x^2+40 x+39$
• $y^2=93 x^6+98 x^5+45 x^4+73 x^3+65 x^2+37 x+66$
• $y^2=67 x^6+84 x^5+83 x^4+53 x^3+60 x^2+67 x+62$
• $y^2=29 x^6+87 x^5+23 x^4+85 x^3+51 x^2+65 x+69$
• $y^2=51 x^5+17 x^4+11 x^3+111 x^2+45 x+107$
• $y^2=35 x^6+35 x^5+82 x^4+44 x^3+17 x^2+83 x+65$
• $y^2=18 x^6+71 x^5+10 x^4+25 x^3+41 x^2+27 x+73$
• $y^2=56 x^6+x^5+84 x^4+76 x^3+108 x^2+64 x+68$
• $y^2=86 x^6+2 x^5+98 x^4+38 x^3+102 x^2+17 x+69$
• $y^2=89 x^6+48 x^5+43 x^4+54 x^3+23 x^2+69 x+82$
• $y^2=98 x^6+42 x^5+66 x^4+87 x^3+29 x^2+14 x+21$
• $y^2=51 x^6+67 x^5+63 x^4+109 x^3+76 x^2+86 x+75$

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 4.0.1026380032.1.

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.y_my	$2$	(not in LMFDB)