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

• Label: 2.113.au_it
• 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:	$1 - 20 x + 227 x^{2} - 2260 x^{3} + 12769 x^{4}$
Frobenius angles:	$\pm0.112341876511$, $\pm0.499249516502$
Angle rank:	$2$ (numerical)
Number field:	4.0.47255824.1
Galois group:	$D_{4}$
Jacobians:	$72$
Isomorphism classes:	216

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$10717$	$163723609$	$2080280856724$	$26579619091396441$	$339457643664576732757$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$94$	$12824$	$1441738$	$163017780$	$18424400894$	$2081956138598$	$235260572575598$	$26584441912759204$	$3004041941375053834$	$339456739063174169864$

Jacobians and polarizations

This isogeny class is principally polarizable and contains the Jacobians of 72 curves (of which all are hyperelliptic):

• $y^2=110 x^6+59 x^5+76 x^4+96 x^3+87 x^2+28 x+13$
• $y^2=39 x^6+46 x^5+x^4+16 x^3+98 x^2+15 x+110$
• $y^2=57 x^6+106 x^5+109 x^4+6 x^3+35 x^2+59 x+28$
• $y^2=61 x^6+101 x^5+30 x^4+103 x^3+75 x^2+9 x+36$
• $y^2=20 x^6+70 x^5+74 x^4+67 x^3+100 x^2+75 x+94$
• $y^2=96 x^6+100 x^5+27 x^4+99 x^3+5 x^2+48 x+110$
• $y^2=63 x^6+112 x^5+105 x^4+74 x^3+58 x^2+47 x+22$
• $y^2=68 x^6+85 x^5+5 x^4+85 x^3+37 x^2+68 x+57$
• $y^2=41 x^6+87 x^5+30 x^4+20 x^3+21 x^2+8 x+92$
• $y^2=8 x^6+13 x^5+87 x^4+30 x^3+69 x^2+94 x+62$
• $y^2=67 x^6+69 x^5+85 x^4+45 x^3+30 x^2+45 x+73$
• $y^2=58 x^6+64 x^5+99 x^4+30 x^3+71 x^2+14 x+87$
• $y^2=88 x^6+34 x^5+64 x^4+48 x^3+13 x^2+5 x+89$
• $y^2=62 x^6+85 x^5+48 x^4+26 x^3+100 x^2+62 x+66$
• $y^2=90 x^6+9 x^5+97 x^4+72 x^3+74 x^2+77 x+100$
• $y^2=86 x^6+61 x^5+35 x^4+105 x^3+85 x^2+90 x+17$
• $y^2=76 x^6+94 x^5+60 x^4+54 x^3+9 x^2+108 x+96$
• $y^2=34 x^6+112 x^5+63 x^4+43 x^3+108 x^2+18 x+107$
• $y^2=3 x^6+45 x^5+92 x^4+56 x^3+38 x^2+41 x+85$
• $y^2=48 x^6+104 x^5+71 x^4+109 x^3+103 x+5$
• and

• $y^2=25 x^6+58 x^5+26 x^4+6 x^2+2 x+47$
• $y^2=58 x^6+3 x^5+101 x^4+16 x^3+55 x^2+65 x+88$
• $y^2=45 x^6+28 x^5+45 x^4+24 x^3+47 x^2+100 x+3$
• $y^2=93 x^6+96 x^5+61 x^4+64 x^3+44 x^2+56 x+111$
• $y^2=85 x^6+9 x^5+65 x^4+4 x^3+73 x^2+109 x+21$
• $y^2=31 x^6+43 x^5+49 x^4+67 x^3+6 x+20$
• $y^2=90 x^6+70 x^5+20 x^4+65 x^3+70 x^2+53 x+36$
• $y^2=20 x^6+104 x^5+64 x^4+60 x^3+37 x^2+94 x+26$
• $y^2=110 x^6+102 x^5+51 x^4+15 x^3+55 x^2+48 x+33$
• $y^2=64 x^6+88 x^5+63 x^4+103 x^3+4 x^2+10 x+77$
• $y^2=65 x^6+63 x^5+52 x^4+52 x^3+85 x^2+68 x+30$
• $y^2=3 x^6+67 x^5+45 x^4+54 x^3+52 x^2+41 x+46$
• $y^2=29 x^6+21 x^5+22 x^4+109 x^3+52 x^2+50 x+20$
• $y^2=34 x^6+58 x^5+6 x^4+62 x^3+31 x^2+98 x+110$
• $y^2=59 x^6+67 x^5+96 x^4+74 x^3+14 x^2+20 x+84$
• $y^2=74 x^6+104 x^5+36 x^4+x^3+34 x^2+94 x+54$
• $y^2=13 x^6+83 x^5+74 x^4+60 x^3+41 x^2+24 x+108$
• $y^2=57 x^6+11 x^5+x^4+28 x^3+40 x^2+52 x+109$
• $y^2=79 x^6+50 x^5+76 x^4+67 x^3+95 x^2+25 x+65$
• $y^2=29 x^6+51 x^5+43 x^4+66 x^3+79 x^2+20 x+72$
• $y^2=49 x^6+16 x^5+92 x^4+55 x^3+16 x^2+14 x+58$
• $y^2=38 x^6+57 x^5+86 x^4+90 x^3+93 x^2+106 x+92$
• $y^2=26 x^6+63 x^5+29 x^4+20 x^3+72 x^2+103 x+41$
• $y^2=33 x^6+85 x^5+55 x^4+10 x^3+5 x^2+21 x+64$
• $y^2=76 x^6+75 x^5+31 x^4+79 x^2+48 x+86$
• $y^2=10 x^6+81 x^5+28 x^4+78 x^3+57 x^2+10 x+90$
• $y^2=69 x^6+63 x^5+111 x^4+26 x^3+94 x^2+33 x+80$
• $y^2=86 x^6+35 x^5+2 x^4+84 x^3+108 x^2+104 x+90$
• $y^2=76 x^6+53 x^5+34 x^4+31 x^3+7 x^2+22 x+54$
• $y^2=85 x^6+107 x^5+8 x^4+110 x^3+102 x^2+53 x+81$
• $y^2=30 x^6+112 x^5+110 x^4+7 x^3+22 x^2+41 x+78$
• $y^2=48 x^6+111 x^5+96 x^4+7 x^3+107 x^2+99 x+59$
• $y^2=9 x^6+90 x^5+48 x^4+55 x^3+10 x^2+23 x+41$
• $y^2=74 x^6+54 x^5+26 x^4+18 x^3+102 x^2+52 x+90$
• $y^2=6 x^6+33 x^5+57 x^4+53 x^3+21 x^2+73 x+76$
• $y^2=80 x^6+54 x^5+100 x^4+111 x^3+34 x^2+33 x+83$
• $y^2=46 x^6+68 x^5+96 x^4+49 x^3+2 x^2+90 x+84$
• $y^2=78 x^6+73 x^5+3 x^4+69 x^3+66 x^2+30 x+32$
• $y^2=25 x^6+92 x^5+33 x^4+21 x^3+62 x^2+5 x+84$
• $y^2=6 x^6+22 x^5+39 x^4+6 x^3+42 x^2+99 x+35$
• $y^2=95 x^6+92 x^5+3 x^4+82 x^3+7 x^2+47 x+23$
• $y^2=88 x^6+69 x^5+58 x^4+54 x^3+87 x^2+27 x+100$
• $y^2=109 x^6+13 x^5+2 x^4+49 x^3+14 x^2+28 x+104$
• $y^2=33 x^6+72 x^5+4 x^4+54 x^3+25 x^2+31 x+40$
• $y^2=13 x^6+22 x^5+97 x^4+99 x^3+84 x^2+71 x+12$
• $y^2=68 x^6+74 x^5+7 x^4+103 x^3+48 x^2+19 x+59$
• $y^2=63 x^6+45 x^5+100 x^4+81 x^3+48 x^2+53 x+45$
• $y^2=71 x^6+104 x^5+20 x^4+51 x^3+67 x^2+2 x+4$
• $y^2=12 x^6+17 x^5+44 x^4+20 x^3+93 x^2+3 x+72$
• $y^2=75 x^6+34 x^5+67 x^4+34 x^3+95 x^2+112 x+40$
• $y^2=106 x^6+47 x^5+39 x^4+77 x^3+98 x^2+41 x+111$
• $y^2=66 x^6+12 x^5+74 x^4+19 x^2+81 x+84$

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 4.0.47255824.1.

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_it	$2$	(not in LMFDB)