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

• Label: 2.113.az_nj
• 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:	$1 - 25 x + 347 x^{2} - 2825 x^{3} + 12769 x^{4}$
Frobenius angles:	$\pm0.165909966308$, $\pm0.400109600639$
Angle rank:	$2$ (numerical)
Number field:	4.0.911126349.1
Galois group:	$D_{4}$
Jacobians:	$60$
Isomorphism classes:	60

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$10267$	$163933189$	$2084732183779$	$26585197554062581$	$339456038840321603632$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$89$	$12839$	$1444823$	$163051995$	$18424313794$	$2081953752023$	$235260599724043$	$26584442360739859$	$3004041936977029349$	$339456738937713236414$

Jacobians and polarizations

This isogeny class is principally polarizable and contains the Jacobians of 60 curves (of which all are hyperelliptic):

• $y^2=88 x^6+99 x^5+81 x^4+48 x^3+16 x^2+41 x+55$
• $y^2=107 x^6+110 x^5+x^4+106 x^3+9 x^2+41 x+3$
• $y^2=2 x^6+50 x^5+74 x^4+71 x^3+5 x^2+102 x+31$
• $y^2=76 x^6+64 x^5+11 x^4+66 x^3+38 x^2+87 x+44$
• $y^2=42 x^6+13 x^5+87 x^4+20 x^3+29 x^2+16 x+7$
• $y^2=31 x^6+63 x^5+63 x^4+18 x^3+66 x^2+9 x+44$
• $y^2=111 x^6+112 x^5+96 x^4+60 x^3+11 x^2+35 x+104$
• $y^2=19 x^6+53 x^5+58 x^4+43 x^3+15 x^2+57 x+34$
• $y^2=107 x^6+107 x^5+2 x^4+51 x^3+49 x+58$
• $y^2=5 x^6+73 x^5+35 x^4+92 x^3+13 x^2+98 x$
• $y^2=84 x^6+82 x^5+88 x^4+90 x^3+69 x^2+18 x+57$
• $y^2=10 x^6+65 x^5+26 x^4+60 x^3+35 x^2+104 x+2$
• $y^2=19 x^6+39 x^5+24 x^4+71 x^3+25 x^2+38 x+20$
• $y^2=78 x^6+91 x^5+95 x^4+45 x^3+87 x^2+40 x+33$
• $y^2=60 x^6+86 x^5+30 x^4+15 x^3+50 x^2+94 x+74$
• $y^2=33 x^6+54 x^5+86 x^4+60 x^3+34 x^2+73 x+96$
• $y^2=43 x^6+61 x^5+81 x^4+30 x^3+24 x^2+71 x+24$
• $y^2=58 x^6+77 x^5+73 x^4+8 x^3+52 x^2+10 x+91$
• $y^2=40 x^6+52 x^5+85 x^4+x^3+23 x^2+42 x+58$
• $y^2=75 x^6+27 x^5+32 x^4+79 x^3+42 x^2+89 x+84$
• and

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

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 4.0.911126349.1.

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_nj	$2$	(not in LMFDB)