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

• Label: 2.113.az_na
• 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:	$1 - 25 x + 338 x^{2} - 2825 x^{3} + 12769 x^{4}$
Frobenius angles:	$\pm0.142953508956$, $\pm0.411301082306$
Angle rank:	$2$ (numerical)
Number field:	4.0.1115187084.1
Galois group:	$D_{4}$
Jacobians:	$64$

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$10258$	$163697164$	$2083757311816$	$26583539397646336$	$339454940306413840018$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$89$	$12821$	$1444148$	$163041825$	$18424254169$	$2081954063522$	$235260607211593$	$26584442422056769$	$3004041938085609524$	$339456738965762503061$

Jacobians and polarizations

This isogeny class is principally polarizable and contains the Jacobians of 64 curves (of which all are hyperelliptic):

• $y^2=60 x^6+37 x^5+59 x^4+83 x^3+92 x^2+31 x+19$
• $y^2=10 x^6+96 x^5+87 x^4+70 x^3+98 x^2+43 x+5$
• $y^2=56 x^6+110 x^5+83 x^4+64 x^3+60 x^2+108 x+89$
• $y^2=64 x^6+89 x^5+47 x^4+50 x^3+55 x^2+102 x+92$
• $y^2=89 x^6+26 x^5+8 x^4+105 x^3+9 x^2+9 x+68$
• $y^2=46 x^6+74 x^5+20 x^4+72 x^3+59 x^2+33 x+80$
• $y^2=50 x^6+49 x^5+51 x^4+26 x^3+33 x^2+26 x+66$
• $y^2=57 x^6+92 x^5+78 x^4+101 x^3+47 x^2+18 x+83$
• $y^2=85 x^6+106 x^5+73 x^4+9 x^3+77 x^2+110 x+89$
• $y^2=101 x^6+44 x^5+105 x^3+60 x^2+26 x+74$
• $y^2=91 x^6+64 x^5+31 x^4+102 x^3+50 x^2+50 x+88$
• $y^2=41 x^6+78 x^5+34 x^4+72 x^3+68 x^2+13 x+17$
• $y^2=51 x^6+68 x^5+43 x^4+78 x^3+22 x^2+78 x+44$
• $y^2=101 x^6+18 x^5+15 x^4+99 x^3+27 x^2+106 x+22$
• $y^2=42 x^6+64 x^5+37 x^4+30 x^3+89 x^2+72 x+69$
• $y^2=93 x^6+28 x^5+94 x^4+24 x^3+75 x^2+58 x+77$
• $y^2=24 x^6+89 x^5+53 x^4+68 x^3+111 x^2+58 x+82$
• $y^2=84 x^6+72 x^5+15 x^4+24 x^3+12 x^2+84 x+6$
• $y^2=105 x^6+32 x^5+75 x^4+92 x^3+71 x^2+33 x+8$
• $y^2=70 x^6+25 x^5+107 x^4+60 x^3+58 x^2+112 x+21$
• and

• $y^2=27 x^6+40 x^5+89 x^4+105 x^3+76 x^2+8 x+90$
• $y^2=5 x^6+29 x^5+103 x^4+112 x^3+60 x^2+x+68$
• $y^2=78 x^6+93 x^5+3 x^4+69 x^3+73 x^2+94 x+103$
• $y^2=26 x^6+47 x^5+19 x^4+21 x^3+17 x^2+43 x+90$
• $y^2=43 x^6+80 x^5+45 x^4+94 x^3+72 x^2+72 x+101$
• $y^2=94 x^6+16 x^5+70 x^4+55 x^3+41 x^2+106 x+112$
• $y^2=28 x^6+78 x^5+102 x^4+44 x^3+44 x^2+80 x+38$
• $y^2=73 x^6+87 x^5+47 x^4+44 x^3+103 x^2+70 x+62$
• $y^2=3 x^6+19 x^5+54 x^4+8 x^3+93 x^2+43 x+35$
• $y^2=85 x^6+70 x^5+76 x^4+3 x^3+53 x^2+25 x+62$
• $y^2=38 x^6+57 x^5+99 x^4+20 x^3+61 x^2+65$
• $y^2=39 x^6+103 x^5+10 x^4+15 x^3+105 x^2+70 x+89$
• $y^2=90 x^6+95 x^5+105 x^4+92 x^3+71 x^2+53 x+40$
• $y^2=66 x^6+7 x^5+x^4+58 x^3+44 x^2+90 x+106$
• $y^2=73 x^6+61 x^5+88 x^4+23 x^3+66 x^2+60 x+13$
• $y^2=34 x^6+52 x^5+90 x^4+71 x^3+49 x^2+82 x+96$
• $y^2=70 x^6+4 x^5+38 x^4+32 x^3+32 x^2+90 x+77$
• $y^2=40 x^6+68 x^5+95 x^4+58 x^3+29 x^2+55 x+84$
• $y^2=91 x^6+49 x^5+44 x^4+9 x^3+14 x^2+81 x+14$
• $y^2=109 x^6+24 x^5+36 x^4+92 x^3+22 x^2+51 x+76$
• $y^2=32 x^6+26 x^5+20 x^4+90 x^3+31 x^2+106 x+59$
• $y^2=92 x^6+48 x^5+108 x^4+100 x^3+21 x^2+51 x+91$
• $y^2=23 x^6+57 x^5+17 x^4+99 x^3+97 x^2+8 x+40$
• $y^2=101 x^6+88 x^5+37 x^4+85 x^3+39 x^2+17 x+72$
• $y^2=74 x^6+65 x^5+5 x^4+74 x^3+23 x^2+18 x+31$
• $y^2=63 x^6+83 x^5+111 x^4+79 x^3+107 x^2+13 x+67$
• $y^2=85 x^6+72 x^5+33 x^4+53 x^3+100 x^2+80 x+18$
• $y^2=85 x^6+76 x^5+31 x^4+5 x^3+86 x^2+100 x+27$
• $y^2=x^6+87 x^5+98 x^4+55 x^3+17 x^2+92 x+65$
• $y^2=37 x^6+52 x^5+63 x^4+73 x^3+58 x^2+56 x+98$
• $y^2=34 x^6+86 x^5+42 x^4+8 x^3+105 x^2+4 x+55$
• $y^2=93 x^6+64 x^5+11 x^4+88 x^3+36 x^2+31 x+24$
• $y^2=81 x^6+62 x^5+70 x^4+86 x^3+16 x^2+109 x+41$
• $y^2=75 x^6+72 x^5+92 x^4+48 x^3+102 x^2+99 x+24$
• $y^2=50 x^6+63 x^5+6 x^4+9 x^3+31 x^2+91 x+70$
• $y^2=5 x^6+53 x^5+75 x^4+102 x^3+31 x^2+51 x+1$
• $y^2=23 x^6+70 x^5+42 x^4+88 x^3+44 x^2+15 x+91$
• $y^2=105 x^6+36 x^5+49 x^4+99 x^3+16 x^2+47 x+81$
• $y^2=23 x^6+77 x^5+6 x^4+18 x^3+79 x^2+39 x+91$
• $y^2=105 x^6+41 x^5+106 x^4+103 x^3+25 x^2+45 x+12$
• $y^2=16 x^6+99 x^5+111 x^4+103 x^3+54 x^2+93 x+47$
• $y^2=70 x^6+44 x^5+4 x^4+14 x^3+5 x^2+21 x+106$
• $y^2=51 x^6+98 x^5+44 x^4+56 x^3+66 x^2+5 x+73$
• $y^2=21 x^6+33 x^5+38 x^4+80 x^3+2 x^2+26 x+24$

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 4.0.1115187084.1.

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_na	$2$	(not in LMFDB)