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

• Label: 2.113.au_jj
• 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:	$1 - 20 x + 243 x^{2} - 2260 x^{3} + 12769 x^{4}$
Frobenius angles:	$\pm0.144382612276$, $\pm0.486677488799$
Angle rank:	$2$ (numerical)
Number field:	4.0.4316482064.1
Galois group:	$D_{4}$
Jacobians:	$110$

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$10733$	$164139769$	$2081665908116$	$26581340613151001$	$339458911250317657093$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$94$	$12856$	$1442698$	$163028340$	$18424469694$	$2081957182822$	$235260587563438$	$26584441909241124$	$3004041938751593674$	$339456739032359564136$

Jacobians and polarizations

This isogeny class is principally polarizable and contains the Jacobians of 110 curves (of which all are hyperelliptic):

• $y^2=45 x^6+77 x^5+29 x^4+46 x^3+54 x^2+94 x+83$
• $y^2=45 x^6+103 x^5+81 x^4+64 x^3+76 x^2+85 x+26$
• $y^2=15 x^6+69 x^5+24 x^4+53 x^3+100 x^2+83 x+45$
• $y^2=55 x^6+10 x^5+65 x^4+40 x^3+58 x^2+17 x+45$
• $y^2=47 x^6+3 x^5+32 x^4+41 x^3+111 x+57$
• $y^2=23 x^6+109 x^4+34 x^3+24 x^2+57 x+66$
• $y^2=86 x^6+71 x^5+52 x^4+64 x^3+56 x^2+64 x+79$
• $y^2=84 x^6+15 x^5+75 x^4+29 x^3+69 x^2+8 x+89$
• $y^2=107 x^6+97 x^5+74 x^4+9 x^3+63 x^2+32 x+54$
• $y^2=85 x^6+104 x^5+41 x^4+x^3+66 x^2+48 x+82$
• $y^2=83 x^6+74 x^5+77 x^4+93 x^3+99 x^2+53 x+4$
• $y^2=106 x^6+86 x^5+39 x^4+5 x^3+37 x^2+94 x+1$
• $y^2=82 x^6+56 x^5+27 x^4+33 x^3+34 x^2+67 x+71$
• $y^2=25 x^6+19 x^5+22 x^4+85 x^3+67 x^2+79 x+20$
• $y^2=77 x^6+59 x^5+4 x^4+97 x^3+23 x^2+61 x+80$
• $y^2=5 x^6+100 x^5+74 x^4+112 x^3+41 x^2+103 x+55$
• $y^2=72 x^6+47 x^5+96 x^4+88 x^3+51 x^2+92 x+85$
• $y^2=83 x^6+39 x^5+31 x^4+73 x^3+3 x^2+74 x+85$
• $y^2=24 x^6+2 x^5+66 x^4+29 x^3+92 x^2+18 x+101$
• $y^2=27 x^6+11 x^5+85 x^4+55 x^3+106 x^2+43 x+29$
• and

• $y^2=48 x^6+17 x^5+2 x^4+83 x^3+110 x^2+67 x+43$
• $y^2=95 x^6+56 x^5+27 x^4+104 x^3+81 x^2+38 x+54$
• $y^2=42 x^6+97 x^5+53 x^4+49 x^3+103 x^2+18 x+32$
• $y^2=58 x^6+61 x^5+56 x^4+51 x^3+112 x^2+24 x+20$
• $y^2=56 x^6+79 x^5+97 x^4+83 x^3+98 x^2+103 x+66$
• $y^2=8 x^6+64 x^5+34 x^4+108 x^3+15 x^2+9 x+95$
• $y^2=19 x^6+55 x^5+5 x^4+89 x^3+79 x^2+91 x+56$
• $y^2=6 x^6+37 x^5+31 x^4+52 x^3+52 x^2+8 x+79$
• $y^2=74 x^6+38 x^5+64 x^4+97 x^3+38 x^2+61 x+63$
• $y^2=19 x^6+60 x^5+111 x^4+96 x^3+81 x^2+56 x+75$
• $y^2=23 x^6+88 x^5+42 x^4+6 x^3+56 x^2+109 x+35$
• $y^2=63 x^6+61 x^5+66 x^4+9 x^3+55 x^2+107 x+13$
• $y^2=58 x^6+10 x^5+25 x^4+45 x^3+31 x^2+51 x+3$
• $y^2=100 x^6+95 x^5+94 x^4+89 x^3+8 x^2+101 x+90$
• $y^2=82 x^6+102 x^5+69 x^4+52 x^3+43 x^2+65 x+52$
• $y^2=19 x^6+88 x^5+103 x^4+85 x^3+68 x^2+60 x+93$
• $y^2=79 x^6+53 x^5+61 x^4+90 x^3+91 x^2+10 x+81$
• $y^2=54 x^6+11 x^5+57 x^4+8 x^3+46 x^2+49 x+22$
• $y^2=46 x^6+x^5+88 x^4+81 x^3+95 x^2+53 x+94$
• $y^2=61 x^6+85 x^5+14 x^4+80 x^3+61 x^2+66 x+93$
• $y^2=100 x^6+8 x^5+51 x^4+38 x^3+29 x^2+41 x+22$
• $y^2=35 x^6+20 x^5+23 x^4+33 x^3+15 x^2+44 x+95$
• $y^2=16 x^6+97 x^5+39 x^4+68 x^3+12 x^2+40 x+48$
• $y^2=57 x^6+31 x^5+18 x^4+30 x^3+39 x^2+10 x+106$
• $y^2=89 x^6+x^5+108 x^4+58 x^3+51 x^2+33 x+32$
• $y^2=109 x^6+69 x^5+92 x^4+66 x^3+71 x^2+89 x+10$
• $y^2=111 x^6+29 x^5+60 x^4+86 x^3+103 x^2+64 x+102$
• $y^2=92 x^6+50 x^5+89 x^4+29 x^3+90 x^2+10 x+31$
• $y^2=31 x^6+28 x^5+62 x^4+31 x^3+31 x^2+50 x+101$
• $y^2=38 x^6+17 x^5+54 x^4+68 x^3+20 x^2+43 x+10$
• $y^2=70 x^6+47 x^5+16 x^4+85 x^3+36 x^2+71 x+104$
• $y^2=55 x^6+54 x^5+80 x^4+x^3+101 x^2+107$
• $y^2=17 x^6+16 x^5+49 x^4+90 x^3+96 x^2+68 x+54$
• $y^2=70 x^6+36 x^5+111 x^4+50 x^3+84 x^2+3 x+40$
• $y^2=62 x^6+109 x^5+77 x^4+83 x^3+73 x^2+96 x+21$
• $y^2=94 x^6+44 x^5+60 x^4+36 x^3+61 x^2+27 x+46$
• $y^2=12 x^6+61 x^5+96 x^4+8 x^3+88 x^2+106 x+48$
• $y^2=46 x^6+71 x^5+92 x^4+42 x^3+38 x^2+76 x+28$
• $y^2=58 x^6+110 x^5+68 x^4+27 x^3+2 x^2+101 x+10$
• $y^2=75 x^6+2 x^5+105 x^4+45 x^3+35 x^2+22 x+89$
• $y^2=104 x^6+95 x^5+82 x^4+20 x^3+87 x^2+68 x+81$
• $y^2=78 x^6+97 x^5+103 x^4+68 x^3+44 x^2+33 x+52$
• $y^2=89 x^6+27 x^5+18 x^4+82 x^3+107 x^2+73 x+14$
• $y^2=93 x^6+104 x^5+4 x^4+77 x^3+62 x^2+89 x+26$
• $y^2=33 x^6+75 x^5+4 x^4+39 x^3+18 x^2+80 x+95$
• $y^2=3 x^6+69 x^5+111 x^4+70 x^3+85 x^2+48 x+90$
• $y^2=34 x^6+65 x^5+70 x^4+31 x^3+79 x^2+67 x+18$
• $y^2=47 x^6+32 x^5+80 x^4+108 x^3+45 x^2+83 x+53$
• $y^2=9 x^6+69 x^5+56 x^4+41 x^3+63 x^2+50 x+93$
• $y^2=x^6+97 x^5+27 x^4+81 x^3+39 x^2+74 x+60$
• $y^2=62 x^6+22 x^5+44 x^4+87 x^3+37 x^2+109 x+55$
• $y^2=39 x^6+17 x^5+33 x^4+25 x^3+74 x^2+32 x+33$
• $y^2=111 x^6+84 x^5+96 x^4+46 x^3+89 x^2+21 x+45$
• $y^2=103 x^6+91 x^5+18 x^4+52 x^3+2 x^2+58 x+25$
• $y^2=55 x^6+11 x^5+41 x^4+47 x^3+30 x^2+84 x+110$
• $y^2=47 x^6+73 x^5+7 x^4+18 x^3+42 x^2+98 x+64$
• $y^2=31 x^6+37 x^5+92 x^4+32 x^3+56 x^2+90 x+79$
• $y^2=5 x^6+31 x^5+58 x^4+11 x^3+18 x^2+36 x+10$
• $y^2=61 x^6+8 x^5+57 x^4+17 x^3+64 x^2+9 x+65$
• $y^2=96 x^6+92 x^5+46 x^4+37 x^3+109 x^2+50 x+42$
• $y^2=52 x^6+29 x^5+61 x^4+60 x^3+42 x^2+15 x+24$
• $y^2=68 x^6+12 x^5+67 x^4+4 x^3+100 x^2+5 x+29$
• $y^2=71 x^6+90 x^5+81 x^4+27 x^3+63 x^2+21 x+105$
• $y^2=11 x^6+35 x^5+6 x^4+97 x^3+x^2+3 x+90$
• $y^2=89 x^6+55 x^5+46 x^4+50 x^3+25 x^2+16 x+35$
• $y^2=90 x^6+81 x^5+19 x^4+92 x^3+34 x^2+92 x+37$
• $y^2=55 x^6+10 x^5+28 x^4+91 x^3+71 x^2+52 x+45$
• $y^2=25 x^6+18 x^5+92 x^4+55 x^3+52 x^2+46 x+21$
• $y^2=22 x^6+77 x^5+3 x^4+66 x^3+31 x^2+54 x+55$
• $y^2=57 x^6+74 x^5+x^4+103 x^2+31 x+108$
• $y^2=46 x^6+13 x^5+49 x^4+16 x^3+45 x^2+65 x+1$
• $y^2=97 x^6+109 x^5+39 x^4+35 x^3+102 x^2+23 x+37$
• $y^2=107 x^6+55 x^5+34 x^4+101 x^3+22 x^2+53 x+6$
• $y^2=24 x^6+93 x^5+67 x^4+107 x^3+49 x^2+54 x+79$
• $y^2=100 x^6+90 x^5+82 x^4+58 x^3+68 x^2+24 x+67$
• $y^2=27 x^6+84 x^5+73 x^4+33 x^3+8 x^2+18 x+59$
• $y^2=72 x^6+24 x^5+65 x^4+56 x^3+44 x^2+17 x+111$
• $y^2=80 x^6+28 x^5+67 x^4+65 x^3+95 x^2+34 x+84$
• $y^2=104 x^6+97 x^5+36 x^4+68 x^3+46 x^2+101 x+72$
• $y^2=42 x^6+54 x^5+68 x^4+73 x^3+104 x^2+112 x+65$
• $y^2=103 x^6+104 x^5+4 x^4+86 x^3+100 x^2+18 x+73$
• $y^2=44 x^6+7 x^5+112 x^4+36 x^3+54 x^2+13 x+38$
• $y^2=9 x^6+29 x^5+65 x^4+76 x^3+46 x^2+98 x+57$
• $y^2=108 x^6+89 x^5+9 x^4+98 x^3+105 x^2+2 x+7$
• $y^2=8 x^6+49 x^5+63 x^4+49 x^3+66 x^2+34 x+19$
• $y^2=89 x^6+28 x^5+47 x^4+8 x^3+44 x^2+44 x+59$
• $y^2=35 x^6+78 x^5+22 x^4+2 x^3+85 x^2+61 x+16$
• $y^2=48 x^6+112 x^5+15 x^4+53 x^3+104 x^2+29 x+20$
• $y^2=54 x^6+92 x^5+18 x^4+61 x^3+85 x^2+54 x+20$
• $y^2=50 x^6+28 x^5+30 x^4+60 x^3+18 x^2+42 x+51$

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 4.0.4316482064.1.

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_jj	$2$	(not in LMFDB)