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

• Label: 2.113.az_nl
• 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:	$1 - 25 x + 349 x^{2} - 2825 x^{3} + 12769 x^{4}$
Frobenius angles:	$\pm0.170978216579$, $\pm0.397415933078$
Angle rank:	$2$ (numerical)
Number field:	4.0.1362053.1
Galois group:	$D_{4}$
Jacobians:	$108$

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$10269$	$163985661$	$2084948844741$	$26585558867525301$	$339456232293279981264$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$89$	$12843$	$1444973$	$163054211$	$18424324294$	$2081953604547$	$235260596793493$	$26584442336312803$	$3004041936735062249$	$339456738932930067678$

Jacobians and polarizations

This isogeny class is principally polarizable and contains the Jacobians of 108 curves (of which all are hyperelliptic):

• $y^2=40 x^6+2 x^5+56 x^4+70 x^3+17 x^2+33 x+51$
• $y^2=25 x^6+61 x^5+105 x^4+91 x^3+37 x^2+42 x+2$
• $y^2=43 x^6+32 x^5+49 x^4+68 x^3+57 x^2+60 x+3$
• $y^2=43 x^6+34 x^5+40 x^4+31 x^3+110 x^2+107 x+39$
• $y^2=78 x^6+111 x^5+28 x^4+73 x^3+105 x^2+35 x+47$
• $y^2=74 x^6+70 x^5+39 x^4+51 x^3+105 x^2+18 x$
• $y^2=74 x^6+44 x^5+15 x^4+29 x^3+40 x^2+78 x+96$
• $y^2=64 x^6+109 x^5+79 x^4+81 x^3+60 x^2+58 x+19$
• $y^2=79 x^6+66 x^5+102 x^4+5 x^3+42 x^2+37 x+32$
• $y^2=51 x^6+91 x^5+16 x^4+15 x^3+35 x^2+68 x+36$
• $y^2=76 x^6+28 x^5+84 x^4+16 x^3+60 x^2+7 x+19$
• $y^2=20 x^6+100 x^5+103 x^4+15 x^3+8 x^2+18 x+112$
• $y^2=38 x^6+33 x^5+72 x^4+105 x^3+34 x^2+17 x+6$
• $y^2=76 x^6+93 x^5+14 x^4+63 x^3+67 x^2+62 x+60$
• $y^2=56 x^6+87 x^5+30 x^4+13 x^3+57 x^2+62 x+4$
• $y^2=48 x^6+x^5+10 x^4+30 x^3+23 x^2+38 x+10$
• $y^2=18 x^6+26 x^5+61 x^4+24 x^3+74 x^2+44 x+80$
• $y^2=89 x^6+108 x^5+15 x^4+112 x^3+7 x^2+47 x+52$
• $y^2=34 x^6+59 x^5+14 x^4+46 x^3+33 x^2+66 x+19$
• $y^2=92 x^6+16 x^5+58 x^4+73 x^3+80 x^2+32 x+47$
• and

• $y^2=5 x^6+36 x^5+106 x^4+65 x^3+80 x^2+62 x+22$
• $y^2=28 x^6+98 x^5+64 x^4+5 x^3+63 x^2+5 x+96$
• $y^2=43 x^6+79 x^5+85 x^4+60 x^3+38 x^2+87 x+105$
• $y^2=36 x^6+31 x^5+43 x^4+23 x^3+73 x^2+82 x+109$
• $y^2=107 x^6+63 x^5+64 x^4+19 x^3+79 x^2+25 x+57$
• $y^2=50 x^6+108 x^4+13 x^3+42 x^2+59 x+12$
• $y^2=58 x^6+35 x^5+104 x^4+46 x^3+55 x^2+5 x+71$
• $y^2=86 x^6+17 x^5+20 x^4+110 x^3+44 x^2+68 x+45$
• $y^2=15 x^6+17 x^5+31 x^4+50 x^3+29 x^2+x+92$
• $y^2=15 x^6+94 x^5+16 x^4+85 x^3+38 x^2+97 x+31$
• $y^2=87 x^6+58 x^5+3 x^4+66 x^3+44 x^2+5 x+31$
• $y^2=54 x^6+17 x^5+7 x^4+45 x^3+55 x^2+6 x+64$
• $y^2=47 x^6+82 x^5+22 x^4+83 x^3+77 x^2+85 x+98$
• $y^2=53 x^6+106 x^5+9 x^4+82 x^3+111 x^2+39 x+36$
• $y^2=81 x^6+65 x^5+30 x^4+107 x^3+108 x^2+39 x+51$
• $y^2=100 x^6+7 x^5+18 x^4+65 x^3+13 x^2+80 x+11$
• $y^2=34 x^6+88 x^5+110 x^4+102 x^3+13 x^2+77 x+43$
• $y^2=84 x^6+97 x^5+29 x^4+61 x^3+16 x+75$
• $y^2=60 x^6+32 x^5+19 x^4+43 x^3+8 x^2+96 x+10$
• $y^2=15 x^6+41 x^5+37 x^4+41 x^3+39 x^2+24 x+67$
• $y^2=73 x^6+112 x^5+32 x^4+48 x^3+6 x^2+100 x+13$
• $y^2=58 x^6+4 x^5+95 x^4+93 x^3+89 x^2+64 x+67$
• $y^2=81 x^6+x^5+25 x^4+20 x^3+30 x^2+38 x+104$
• $y^2=35 x^6+61 x^5+71 x^4+100 x^3+47 x^2+65 x+93$
• $y^2=86 x^6+21 x^5+71 x^4+31 x^3+106 x^2+22 x+96$
• $y^2=13 x^6+49 x^5+69 x^4+32 x^3+5 x^2+33 x+101$
• $y^2=48 x^6+56 x^5+76 x^4+78 x^3+4 x^2+78 x+20$
• $y^2=48 x^6+71 x^5+73 x^4+109 x^3+10 x^2+101 x+19$
• $y^2=59 x^6+6 x^5+5 x^4+91 x^3+96 x^2+68 x+8$
• $y^2=40 x^6+54 x^5+37 x^4+103 x^3+104 x^2+85 x+20$
• $y^2=99 x^6+76 x^5+38 x^4+104 x^3+54 x^2+38 x+98$
• $y^2=3 x^6+107 x^5+32 x^4+21 x^3+100 x^2+38 x+108$
• $y^2=2 x^6+13 x^5+30 x^4+76 x^3+77 x^2+9 x+24$
• $y^2=77 x^6+112 x^4+110 x^2+70 x+43$
• $y^2=79 x^6+53 x^5+53 x^4+95 x^3+32 x^2+69 x+6$
• $y^2=45 x^6+105 x^5+22 x^4+85 x^3+80 x^2+60 x+106$
• $y^2=54 x^6+30 x^5+19 x^4+34 x^3+13 x^2+56 x+81$
• $y^2=79 x^6+26 x^5+60 x^4+24 x^3+63 x^2+41 x+54$
• $y^2=16 x^6+69 x^5+50 x^4+33 x^3+83 x^2+98 x+5$
• $y^2=98 x^6+2 x^5+25 x^4+27 x^3+24 x^2+98 x+19$
• $y^2=31 x^6+48 x^5+53 x^4+108 x^3+99 x^2+73 x+86$
• $y^2=88 x^6+98 x^5+95 x^4+28 x^3+71 x^2+103 x+53$
• $y^2=3 x^6+x^5+4 x^4+45 x^3+88 x^2+6 x+70$
• $y^2=24 x^6+99 x^5+61 x^4+83 x^3+65 x^2+22 x+44$
• $y^2=55 x^6+97 x^5+100 x^4+108 x^3+82 x^2+15 x+10$
• $y^2=23 x^6+37 x^5+39 x^4+67 x^3+40 x^2+26 x+61$
• $y^2=68 x^6+112 x^5+67 x^4+66 x^3+31 x^2+14 x+112$
• $y^2=46 x^6+85 x^5+20 x^4+77 x^3+26 x^2+55 x+9$
• $y^2=33 x^6+64 x^5+26 x^4+9 x^3+75 x^2+49 x+20$
• $y^2=66 x^6+3 x^5+93 x^4+103 x^3+11 x^2+31 x+42$
• $y^2=67 x^6+20 x^5+105 x^4+68 x^3+41 x^2+68 x+78$
• $y^2=20 x^6+19 x^5+11 x^4+62 x^3+49 x^2+95 x+101$
• $y^2=52 x^6+95 x^5+15 x^4+112 x^3+87 x^2+101 x+70$
• $y^2=10 x^6+36 x^5+112 x^4+47 x^3+92 x^2+101 x+55$
• $y^2=84 x^6+40 x^5+96 x^4+54 x^3+50 x^2+80 x+21$
• $y^2=103 x^6+91 x^5+94 x^4+23 x^3+38 x^2+54 x+79$
• $y^2=105 x^6+63 x^5+77 x^4+44 x^3+37 x^2+110 x+24$
• $y^2=48 x^6+105 x^5+73 x^4+49 x^3+92 x^2+38 x+79$
• $y^2=27 x^6+108 x^5+93 x^4+67 x^3+77 x^2+40 x+58$
• $y^2=65 x^6+39 x^5+54 x^4+46 x^3+40 x^2+46 x+96$
• $y^2=38 x^6+85 x^5+85 x^4+89 x^3+92 x^2+17 x+69$
• $y^2=94 x^6+54 x^5+16 x^4+72 x^3+40 x^2+35 x+66$
• $y^2=93 x^6+66 x^5+87 x^4+110 x^3+37 x^2+70 x+35$
• $y^2=94 x^6+58 x^5+99 x^4+68 x^3+48 x^2+47 x+103$
• $y^2=47 x^5+15 x^4+14 x^3+72 x^2+42 x+3$
• $y^2=10 x^6+23 x^5+28 x^4+35 x^3+46 x^2+47 x+28$
• $y^2=105 x^6+64 x^5+43 x^4+61 x^3+51 x^2+44 x+11$
• $y^2=20 x^6+2 x^5+43 x^4+25 x^3+19 x^2+8 x+104$
• $y^2=16 x^6+56 x^5+45 x^4+99 x^3+71 x^2+26 x+102$
• $y^2=10 x^6+38 x^5+17 x^4+26 x^3+92 x^2+110 x+4$
• $y^2=3 x^6+54 x^5+104 x^4+98 x^3+73 x^2+25 x+95$
• $y^2=40 x^6+16 x^5+29 x^4+76 x^3+18 x^2+94 x+19$
• $y^2=64 x^6+99 x^5+76 x^4+64 x^3+68 x^2+49 x+70$
• $y^2=20 x^6+16 x^5+12 x^4+89 x^3+5 x^2+45 x+91$
• $y^2=6 x^6+8 x^5+16 x^4+44 x^3+57 x^2+106 x+108$
• $y^2=84 x^6+59 x^5+33 x^4+55 x^3+104 x^2+8 x+43$
• $y^2=78 x^6+26 x^5+45 x^4+16 x^3+38 x^2+24 x+37$
• $y^2=5 x^6+18 x^5+35 x^4+25 x^3+46 x^2+13 x+23$
• $y^2=34 x^6+76 x^5+75 x^4+64 x^3+93 x^2+85 x+1$
• $y^2=5 x^6+44 x^5+4 x^4+84 x^3+9 x^2+69 x+27$
• $y^2=88 x^6+73 x^5+47 x^4+78 x^3+33 x^2+46 x+74$
• $y^2=38 x^6+18 x^5+92 x^4+45 x^3+72 x^2+69 x+79$
• $y^2=19 x^6+28 x^5+24 x^4+86 x^3+108 x^2+13 x+67$
• $y^2=78 x^6+7 x^5+37 x^4+x^3+82 x^2+48 x+26$
• $y^2=84 x^6+52 x^5+71 x^4+57 x^3+52 x^2+104 x+21$
• $y^2=47 x^6+7 x^5+75 x^4+49 x^3+55 x^2+39 x+68$
• $y^2=60 x^6+35 x^5+93 x^4+43 x^3+45 x^2+25 x+27$
• $y^2=31 x^6+97 x^5+21 x^4+89 x^3+51 x^2+108 x+76$

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 4.0.1362053.1.

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.z_nl	$2$	(not in LMFDB)