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

• Label: 2.113.au_if
• 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:	$1 - 20 x + 213 x^{2} - 2260 x^{3} + 12769 x^{4}$
Frobenius angles:	$\pm0.0776925923112$, $\pm0.509435948749$
Angle rank:	$2$ (numerical)
Number field:	4.0.152219249.1
Galois group:	$D_{4}$
Jacobians:	$96$
Isomorphism classes:	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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$10703$	$163359889$	$2079069223616$	$26577975833400761$	$339455760692254718743$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$94$	$12796$	$1440898$	$163007700$	$18424298694$	$2081954286622$	$235260545937238$	$26584441733606244$	$3004041940928922274$	$339456739055628035436$

Jacobians and polarizations

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

• $y^2=108 x^6+73 x^5+108 x^4+98 x^3+107 x^2+26 x+101$
• $y^2=51 x^6+61 x^5+5 x^4+24 x^3+61 x^2+48 x+43$
• $y^2=109 x^6+7 x^5+79 x^4+107 x^2+100 x+76$
• $y^2=37 x^6+19 x^5+89 x^4+15 x^3+14 x+62$
• $y^2=42 x^6+67 x^5+65 x^4+79 x^3+47 x^2+50 x+33$
• $y^2=42 x^6+98 x^5+2 x^4+61 x^3+62 x^2+31 x+79$
• $y^2=33 x^6+107 x^5+54 x^4+92 x^3+20 x^2+98 x+11$
• $y^2=31 x^6+33 x^5+75 x^4+40 x^3+26 x^2+63 x+55$
• $y^2=75 x^6+91 x^5+93 x^4+32 x^3+72 x^2+21 x+90$
• $y^2=37 x^6+89 x^5+59 x^4+102 x^3+55 x^2+4 x+103$
• $y^2=72 x^6+90 x^5+6 x^4+89 x^3+91 x^2+5 x+55$
• $y^2=66 x^6+18 x^5+66 x^4+39 x^3+88 x^2+57 x+21$
• $y^2=31 x^6+110 x^5+72 x^4+79 x^3+76 x^2+27 x+90$
• $y^2=52 x^6+12 x^5+53 x^4+95 x^3+10 x^2+31 x+87$
• $y^2=10 x^6+62 x^5+46 x^4+59 x^3+87 x^2+77 x+68$
• $y^2=79 x^6+99 x^5+70 x^4+17 x^3+99 x^2+4 x+87$
• $y^2=59 x^6+112 x^5+83 x^4+104 x^3+26 x^2+50 x+79$
• $y^2=94 x^6+61 x^5+66 x^4+21 x^3+41 x^2+6 x+67$
• $y^2=70 x^6+27 x^5+56 x^4+46 x^3+53 x^2+97 x+48$
• $y^2=23 x^6+109 x^5+80 x^4+32 x^3+x^2+57 x+79$
• and

• $y^2=78 x^6+46 x^5+48 x^4+112 x^3+30 x^2+49 x+62$
• $y^2=80 x^6+29 x^5+65 x^4+64 x^3+17 x^2+31 x+107$
• $y^2=3 x^6+17 x^4+53 x^3+72 x^2+53 x+68$
• $y^2=27 x^6+65 x^5+16 x^4+62 x^3+72 x^2+94 x+42$
• $y^2=26 x^6+68 x^5+81 x^4+79 x^3+83 x^2+55 x+84$
• $y^2=62 x^6+87 x^5+59 x^4+111 x^3+39 x^2+112 x+43$
• $y^2=10 x^6+36 x^5+16 x^4+70 x^3+45 x^2+67 x+10$
• $y^2=36 x^6+35 x^5+63 x^4+52 x^3+48 x^2+32$
• $y^2=55 x^6+57 x^5+111 x^4+96 x^3+80 x^2+81 x+54$
• $y^2=54 x^6+12 x^5+100 x^4+109 x^3+31 x^2+112 x+24$
• $y^2=38 x^6+45 x^5+58 x^4+51 x^3+55 x^2+42 x+67$
• $y^2=25 x^6+97 x^5+19 x^4+51 x^3+53 x^2+18 x+33$
• $y^2=6 x^6+101 x^5+107 x^4+30 x^3+97 x^2+78 x+1$
• $y^2=2 x^6+57 x^5+108 x^4+11 x^3+56 x^2+101 x+22$
• $y^2=91 x^6+42 x^5+9 x^4+68 x^3+49 x^2+25 x+24$
• $y^2=100 x^6+92 x^5+89 x^4+60 x^3+53 x^2+98 x+44$
• $y^2=65 x^6+92 x^5+13 x^4+82 x^3+6 x^2+37 x+94$
• $y^2=38 x^6+40 x^5+92 x^4+9 x^3+108 x^2+61 x+11$
• $y^2=97 x^6+109 x^5+97 x^4+30 x^3+107 x^2+79 x+23$
• $y^2=33 x^6+73 x^5+92 x^4+71 x^3+8 x+10$
• $y^2=2 x^6+54 x^5+55 x^4+51 x^3+54 x^2+6 x+47$
• $y^2=86 x^6+65 x^5+38 x^4+104 x^3+66 x^2+88 x+35$
• $y^2=83 x^6+10 x^5+46 x^4+14 x^3+17 x^2+7 x+98$
• $y^2=90 x^6+2 x^5+86 x^4+24 x^3+52 x^2+41 x+12$
• $y^2=84 x^6+29 x^5+42 x^4+88 x^3+82 x^2+41 x+56$
• $y^2=75 x^6+3 x^5+82 x^4+104 x^3+39 x^2+74 x+44$
• $y^2=20 x^6+26 x^5+14 x^4+26 x^3+89 x^2+79 x+74$
• $y^2=59 x^6+14 x^4+47 x^3+13 x^2+9 x+82$
• $y^2=75 x^6+70 x^5+48 x^4+85 x^3+71 x^2+22 x+30$
• $y^2=92 x^6+104 x^5+66 x^4+11 x^3+29 x^2+26 x+107$
• $y^2=89 x^6+22 x^5+86 x^4+75 x^3+84 x^2+110 x+10$
• $y^2=77 x^6+10 x^5+111 x^4+4 x^3+38 x^2+96 x+43$
• $y^2=12 x^6+103 x^5+82 x^4+84 x^3+7 x^2+65 x+44$
• $y^2=56 x^6+15 x^5+20 x^4+19 x^3+109 x^2+8 x+47$
• $y^2=27 x^6+14 x^5+55 x^4+89 x^3+92 x^2+48 x+10$
• $y^2=108 x^6+59 x^5+43 x^4+x^3+4 x^2+26 x+8$
• $y^2=59 x^6+45 x^5+38 x^4+14 x^3+46 x^2+103 x+42$
• $y^2=96 x^6+94 x^5+94 x^4+93 x^3+6 x^2+65 x+60$
• $y^2=x^6+104 x^5+62 x^4+82 x^3+80 x^2+80 x+106$
• $y^2=11 x^6+101 x^5+69 x^4+28 x^3+26 x^2+88 x+28$
• $y^2=108 x^6+92 x^5+94 x^4+x^3+97 x^2+37 x+90$
• $y^2=97 x^6+103 x^5+32 x^4+75 x^3+59 x^2+90 x+67$
• $y^2=19 x^6+65 x^5+110 x^4+62 x^3+107 x^2+97 x+7$
• $y^2=104 x^6+81 x^5+58 x^4+77 x^3+74 x^2+56 x+8$
• $y^2=104 x^6+x^5+45 x^4+86 x^3+38 x^2+49 x+92$
• $y^2=61 x^6+81 x^5+105 x^4+11 x^3+55 x^2+58 x+77$
• $y^2=2 x^6+65 x^5+2 x^4+97 x^3+76 x^2+70 x+4$
• $y^2=58 x^6+62 x^5+58 x^4+51 x^3+85 x^2+67 x+30$
• $y^2=12 x^6+75 x^5+33 x^4+48 x^3+14 x^2+108 x+27$
• $y^2=47 x^6+60 x^5+45 x^4+100 x^3+77 x^2+112 x+6$
• $y^2=22 x^6+35 x^5+98 x^4+52 x^3+82 x^2+100 x+50$
• $y^2=37 x^6+56 x^5+57 x^4+105 x^3+73 x^2+83 x+26$
• $y^2=36 x^6+91 x^5+71 x^4+43 x^3+110 x^2+4 x+46$
• $y^2=22 x^6+51 x^5+100 x^4+51 x^3+38 x+2$
• $y^2=97 x^6+71 x^5+68 x^4+75 x^3+9 x^2+25 x+112$
• $y^2=57 x^6+94 x^5+6 x^4+34 x^3+12 x^2+100 x+66$
• $y^2=71 x^6+55 x^5+91 x^4+30 x^3+49 x^2+52 x+92$
• $y^2=19 x^6+78 x^5+9 x^4+35 x^3+87 x^2+14 x+35$
• $y^2=39 x^6+6 x^5+83 x^4+110 x^3+25 x^2+32 x+47$
• $y^2=34 x^6+57 x^5+96 x^3+30 x^2+108 x+67$
• $y^2=109 x^6+12 x^5+16 x^4+63 x^3+71 x^2+19 x+46$
• $y^2=65 x^6+38 x^5+96 x^4+15 x^3+87 x^2+34 x+52$
• $y^2=95 x^6+28 x^5+50 x^4+55 x^3+62 x^2+61 x+29$
• $y^2=52 x^6+11 x^5+65 x^4+50 x^3+x^2+109 x+58$
• $y^2=2 x^6+39 x^5+59 x^4+59 x^3+52 x^2+56 x+110$
• $y^2=79 x^6+11 x^5+40 x^3+58 x^2+55 x+27$
• $y^2=43 x^6+89 x^5+5 x^4+89 x^3+68 x^2+43 x+4$
• $y^2=87 x^6+61 x^5+90 x^4+24 x^3+45 x^2+92 x+46$
• $y^2=97 x^6+54 x^5+13 x^4+98 x^3+55 x^2+18 x+3$
• $y^2=103 x^6+24 x^5+52 x^4+51 x^3+22 x^2+47 x+78$
• $y^2=2 x^6+68 x^5+107 x^4+11 x^3+39 x^2+23 x+30$
• $y^2=103 x^6+40 x^5+77 x^4+107 x^3+50 x^2+31 x+27$
• $y^2=40 x^6+58 x^5+12 x^4+18 x^3+90 x^2+79 x+94$
• $y^2=70 x^6+27 x^5+46 x^4+44 x^3+79 x^2+11 x+7$
• $y^2=24 x^6+107 x^5+100 x^4+30 x^3+31 x^2+36 x+45$
• $y^2=13 x^6+105 x^5+3 x^4+25 x^3+67 x^2+82 x+65$

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 4.0.152219249.1.

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_if	$2$	(not in LMFDB)