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

• Label: 2.113.av_iz
• 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:	$1 - 21 x + 233 x^{2} - 2373 x^{3} + 12769 x^{4}$
Frobenius angles:	$\pm0.0757446595926$, $\pm0.494927269661$
Angle rank:	$2$ (numerical)
Number field:	4.0.1935787581.1
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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$10609$	$163346773$	$2079500060425$	$26577871334953029$	$339454481016393890704$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$93$	$12795$	$1441197$	$163007059$	$18424229238$	$2081954213835$	$235260554367141$	$26584441712171299$	$3004041939361818021$	$339456739055262424350$

Jacobians and polarizations

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

• $y^2=103 x^6+112 x^5+80 x^4+7 x^3+47 x^2+11 x+23$
• $y^2=36 x^6+9 x^5+37 x^4+104 x^3+80 x^2+41 x+101$
• $y^2=42 x^6+12 x^5+68 x^4+22 x^3+14 x^2+87 x+33$
• $y^2=79 x^6+78 x^5+71 x^4+13 x^3+81 x^2+12 x+101$
• $y^2=36 x^6+106 x^5+78 x^4+37 x^3+90 x^2+72 x+74$
• $y^2=24 x^6+24 x^5+91 x^4+107 x^3+9 x^2+49 x+90$
• $y^2=17 x^6+94 x^5+75 x^4+16 x^3+39 x^2+94 x+5$
• $y^2=8 x^6+77 x^5+101 x^4+51 x^3+20 x^2+95 x+35$
• $y^2=19 x^6+89 x^5+71 x^4+52 x^3+17 x^2+16 x+82$
• $y^2=18 x^6+52 x^5+31 x^4+45 x^3+108 x^2+28 x+89$
• $y^2=4 x^6+80 x^5+74 x^4+17 x^3+102 x^2+11 x+7$
• $y^2=53 x^6+110 x^5+24 x^4+15 x^3+80 x^2+30 x+46$
• $y^2=75 x^6+80 x^5+54 x^4+34 x^3+63 x^2+69 x+49$
• $y^2=85 x^6+18 x^5+27 x^4+44 x^3+52 x^2+75 x+86$
• $y^2=92 x^6+2 x^5+89 x^4+62 x^3+65 x^2+75 x+102$
• $y^2=7 x^6+74 x^5+91 x^4+33 x^3+6 x^2+100 x+62$
• $y^2=26 x^6+76 x^5+46 x^4+10 x^3+86 x^2+x+56$
• $y^2=60 x^6+24 x^5+92 x^4+29 x^3+8 x^2+14 x+57$
• $y^2=55 x^6+23 x^5+90 x^4+31 x^3+84 x^2+24 x+8$
• $y^2=68 x^6+21 x^5+98 x^4+105 x^3+30 x^2+83 x+87$
• and

• $y^2=24 x^6+19 x^5+105 x^4+108 x^3+35 x^2+93 x+26$
• $y^2=18 x^6+94 x^5+16 x^4+55 x^3+101 x^2+46 x+12$
• $y^2=20 x^6+51 x^5+112 x^4+15 x^3+106 x^2+50 x+44$
• $y^2=77 x^6+101 x^5+95 x^4+24 x^3+74 x^2+109 x+100$
• $y^2=12 x^6+26 x^5+11 x^4+2 x^3+72 x^2+89 x+70$
• $y^2=106 x^6+109 x^5+3 x^4+74 x^3+90 x^2+47 x+46$
• $y^2=100 x^6+96 x^5+86 x^4+67 x^3+79 x^2+9 x+108$
• $y^2=59 x^6+55 x^5+103 x^4+20 x^3+92 x^2+37 x+74$
• $y^2=4 x^6+28 x^5+5 x^4+101 x^3+26 x^2+37 x+108$
• $y^2=110 x^6+48 x^5+48 x^4+22 x^3+59 x^2+6 x+24$
• $y^2=23 x^6+85 x^5+100 x^4+111 x^3+28 x^2+x+104$
• $y^2=62 x^6+14 x^5+49 x^4+28 x^3+84 x^2+111 x+17$
• $y^2=27 x^6+6 x^5+106 x^4+59 x^3+52 x^2+40 x+92$
• $y^2=104 x^6+108 x^5+36 x^4+92 x^3+49 x^2+5 x+41$
• $y^2=82 x^5+90 x^4+86 x^3+51 x^2+70 x+93$
• $y^2=76 x^6+19 x^5+59 x^4+105 x^3+107 x^2+6 x+48$
• $y^2=74 x^6+64 x^5+56 x^4+90 x^3+22 x^2+29 x+21$
• $y^2=93 x^6+112 x^5+101 x^4+108 x^3+59 x^2+26 x+36$
• $y^2=x^6+53 x^5+29 x^4+96 x^3+35 x^2+17 x+60$
• $y^2=46 x^6+61 x^5+3 x^4+74 x^3+98 x^2+79 x+23$
• $y^2=31 x^6+94 x^5+32 x^4+7 x^3+34 x+24$
• $y^2=8 x^6+109 x^5+63 x^4+19 x^3+51 x^2+36 x+100$
• $y^2=66 x^6+3 x^5+27 x^4+56 x^3+7 x^2+86 x+27$
• $y^2=7 x^6+47 x^5+71 x^4+94 x^3+49 x^2+69 x+15$
• $y^2=73 x^6+39 x^5+43 x^4+69 x^3+92 x^2+35 x+107$
• $y^2=84 x^6+21 x^5+82 x^4+6 x^3+74 x^2+75 x+23$
• $y^2=34 x^6+17 x^5+36 x^4+73 x^3+21 x^2+44 x+18$
• $y^2=76 x^6+90 x^5+88 x^4+96 x^3+26 x^2+109 x+4$
• $y^2=103 x^6+87 x^5+40 x^4+100 x^3+79 x^2+49 x+72$
• $y^2=77 x^6+37 x^5+69 x^4+24 x^3+5 x^2+42 x+39$
• $y^2=98 x^6+109 x^5+98 x^4+6 x^3+64 x^2+108 x+110$
• $y^2=8 x^6+25 x^5+38 x^4+19 x^3+5 x+96$
• $y^2=37 x^6+7 x^5+48 x^4+17 x^3+107 x^2+21 x+58$
• $y^2=73 x^6+23 x^5+42 x^4+47 x^3+28 x^2+112 x+95$
• $y^2=7 x^6+108 x^5+109 x^4+74 x^3+25 x^2+50 x+19$
• $y^2=34 x^6+53 x^5+65 x^4+89 x^3+4 x^2+63 x+95$
• $y^2=37 x^6+23 x^5+100 x^4+22 x^3+33 x^2+x+111$
• $y^2=73 x^6+29 x^5+105 x^4+104 x^3+103 x^2+10 x+92$
• $y^2=23 x^6+15 x^5+85 x^4+65 x^3+19 x^2+22 x+93$
• $y^2=83 x^6+103 x^5+35 x^4+109 x^3+26 x^2+26 x+106$
• $y^2=42 x^6+28 x^5+58 x^4+106 x^3+9 x^2+63 x+101$
• $y^2=5 x^6+44 x^5+37 x^4+40 x^3+101 x^2+103 x+56$
• $y^2=59 x^6+33 x^5+88 x^4+21 x^3+48 x^2+110 x+3$
• $y^2=63 x^6+82 x^5+102 x^4+97 x^3+15 x^2+111 x+20$
• $y^2=83 x^6+88 x^5+4 x^4+111 x^3+31 x^2+52 x+54$
• $y^2=74 x^6+50 x^5+75 x^4+5 x^3+27 x^2+28 x+99$
• $y^2=75 x^6+3 x^5+72 x^4+19 x^3+9 x^2+20 x+42$
• $y^2=26 x^6+46 x^5+33 x^4+98 x^3+75 x^2+107 x+7$
• $y^2=30 x^6+59 x^5+40 x^4+34 x^3+42 x^2+93 x+84$
• $y^2=5 x^6+81 x^5+84 x^4+86 x^3+68 x^2+55 x+101$
• $y^2=44 x^6+110 x^5+11 x^4+79 x^3+110 x^2+2 x+46$
• $y^2=44 x^6+112 x^5+79 x^4+87 x^3+49 x^2+111 x+25$
• $y^2=12 x^6+106 x^5+99 x^4+71 x^3+32 x^2+42 x+66$
• $y^2=91 x^6+36 x^5+72 x^4+18 x^3+99 x^2+55 x+50$
• $y^2=112 x^6+31 x^5+89 x^4+46 x^3+108 x^2+58 x+10$
• $y^2=106 x^6+32 x^5+55 x^4+9 x^3+64 x^2+38 x+92$
• $y^2=28 x^6+99 x^5+17 x^4+60 x^3+58 x^2+77 x+59$
• $y^2=53 x^6+71 x^5+109 x^4+98 x^3+28 x^2+18 x+71$
• $y^2=85 x^6+47 x^5+80 x^4+106 x^3+70 x^2+65 x+32$
• $y^2=88 x^6+52 x^5+74 x^4+66 x^3+62 x^2+61 x+39$
• $y^2=27 x^6+99 x^5+66 x^4+35 x^3+102 x^2+x+108$
• $y^2=9 x^6+57 x^5+105 x^4+63 x^3+46 x^2+17 x+30$
• $y^2=58 x^6+44 x^5+22 x^4+51 x^3+20 x^2+55 x+62$
• $y^2=89 x^6+21 x^5+30 x^4+26 x^3+20 x^2+13 x+94$
• $y^2=27 x^6+44 x^5+74 x^4+112 x^3+92 x^2+3 x+37$
• $y^2=34 x^6+78 x^5+20 x^4+52 x^3+7 x^2+31 x+59$
• $y^2=95 x^6+35 x^5+38 x^4+61 x^3+93 x^2+71 x+107$
• $y^2=108 x^6+72 x^5+110 x^4+84 x^3+108 x^2+15 x+83$
• $y^2=11 x^6+2 x^5+65 x^4+46 x^3+33 x^2+107 x+70$
• $y^2=90 x^6+17 x^5+100 x^4+8 x^3+83 x^2+26 x+47$
• $y^2=39 x^6+9 x^5+20 x^4+19 x^3+26 x^2+94 x+58$
• $y^2=85 x^6+22 x^5+20 x^4+41 x^3+91 x^2+45 x+9$
• $y^2=26 x^6+x^5+94 x^4+96 x^3+56 x^2+74 x+12$
• $y^2=18 x^6+14 x^5+57 x^4+89 x^3+103 x^2+83 x+35$
• $y^2=38 x^6+103 x^5+40 x^4+41 x^3+64 x^2+49 x+82$
• $y^2=9 x^6+13 x^5+83 x^4+103 x^3+101 x^2+81 x+89$

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 4.0.1935787581.1.

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.v_iz	$2$	(not in LMFDB)