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

• Label: 2.113.az_ne
• 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:	$1 - 25 x + 342 x^{2} - 2825 x^{3} + 12769 x^{4}$
Frobenius angles:	$\pm0.153225289375$, $\pm0.406497574994$
Angle rank:	$2$ (numerical)
Number field:	4.0.1040054204.1
Galois group:	$D_{4}$
Jacobians:	$52$
Isomorphism classes:	52

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$10262$	$163802044$	$2084190567704$	$26584282870556096$	$339455474603529653782$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$89$	$12829$	$1444448$	$163046385$	$18424283169$	$2081953996498$	$235260605059793$	$26584442405638689$	$3004041937614762224$	$339456738952411328589$

Jacobians and polarizations

This isogeny class is principally polarizable and contains the Jacobians of 52 curves (of which all are hyperelliptic):

• $y^2=47 x^6+74 x^5+34 x^4+95 x^3+53 x^2+46 x+22$
• $y^2=89 x^6+21 x^5+74 x^4+65 x^3+57 x^2+71 x+8$
• $y^2=3 x^6+56 x^5+101 x^4+94 x^3+101 x^2+60 x+68$
• $y^2=28 x^6+78 x^5+4 x^4+38 x^3+73 x^2+82 x+93$
• $y^2=102 x^6+14 x^5+49 x^4+105 x^3+9 x^2+112 x+106$
• $y^2=78 x^6+13 x^5+109 x^4+96 x^3+81 x^2+62 x+79$
• $y^2=21 x^6+83 x^5+110 x^4+71 x^3+26 x^2+44 x+45$
• $y^2=12 x^6+11 x^5+70 x^4+92 x^3+66 x^2+85 x+28$
• $y^2=57 x^6+54 x^5+38 x^4+43 x^3+66 x^2+66 x+20$
• $y^2=85 x^6+26 x^5+86 x^4+26 x^3+77 x^2+92 x+106$
• $y^2=3 x^6+12 x^5+108 x^4+34 x^3+12 x^2+52 x+59$
• $y^2=50 x^6+42 x^5+72 x^4+50 x^3+4 x^2+68$
• $y^2=110 x^6+28 x^5+22 x^4+63 x^3+61 x^2+14 x+67$
• $y^2=38 x^6+104 x^5+86 x^4+9 x^3+62 x^2+22 x+61$
• $y^2=13 x^6+45 x^5+8 x^4+36 x^3+87 x^2+25 x+23$
• $y^2=72 x^6+24 x^5+29 x^4+79 x^3+9 x^2+30 x+43$
• $y^2=107 x^6+13 x^5+105 x^4+83 x^3+40 x^2+29 x+26$
• $y^2=10 x^6+92 x^5+86 x^4+60 x^3+93 x^2+95 x+100$
• $y^2=110 x^6+x^5+26 x^4+91 x^3+17 x^2+21 x+53$
• $y^2=104 x^6+33 x^5+56 x^4+65 x^3+63 x^2+25 x+67$
• and

• $y^2=14 x^6+77 x^5+53 x^4+74 x^3+16 x^2+98 x+73$
• $y^2=6 x^6+109 x^5+48 x^4+44 x^3+54 x^2+36 x+43$
• $y^2=79 x^6+24 x^5+74 x^4+84 x^3+22 x^2+62 x+68$
• $y^2=78 x^6+20 x^5+73 x^4+67 x^3+18 x^2+32 x+34$
• $y^2=90 x^6+77 x^5+8 x^4+14 x^3+66 x^2+20 x+69$
• $y^2=67 x^6+41 x^5+46 x^4+23 x^3+68 x^2+18 x$
• $y^2=85 x^6+57 x^5+65 x^4+111 x^3+7 x^2+85 x+37$
• $y^2=65 x^6+97 x^5+26 x^4+74 x^3+40 x^2+75 x+60$
• $y^2=82 x^6+8 x^5+112 x^3+110 x^2+90 x+65$
• $y^2=95 x^6+57 x^5+79 x^4+71 x^3+38 x^2+106 x+72$
• $y^2=6 x^6+81 x^5+54 x^4+74 x^3+34 x+111$
• $y^2=23 x^6+93 x^5+10 x^3+34 x^2+46 x+16$
• $y^2=12 x^6+35 x^5+19 x^4+57 x^3+100 x^2+44 x+68$
• $y^2=19 x^6+72 x^5+100 x^4+52 x^3+16 x^2+47 x+74$
• $y^2=71 x^6+37 x^5+12 x^4+36 x^3+22 x^2+91 x+80$
• $y^2=51 x^6+71 x^5+94 x^4+57 x^3+108 x^2+96 x+31$
• $y^2=83 x^6+74 x^5+12 x^4+86 x^3+5 x^2+90 x+47$
• $y^2=84 x^6+10 x^5+40 x^4+75 x^3+30 x^2+23 x+34$
• $y^2=5 x^6+41 x^5+67 x^4+13 x^3+46 x^2+104 x+48$
• $y^2=91 x^6+27 x^5+103 x^4+107 x^3+44 x^2+92 x+88$
• $y^2=26 x^6+98 x^5+33 x^4+92 x^3+48 x^2+54 x+37$
• $y^2=82 x^6+37 x^5+81 x^4+13 x^3+58 x^2+69 x+31$
• $y^2=82 x^6+9 x^5+52 x^4+92 x^3+55 x^2+20 x+2$
• $y^2=5 x^6+11 x^5+57 x^4+105 x^3+89 x^2+62 x+89$
• $y^2=73 x^6+106 x^5+82 x^4+41 x^3+9 x^2+40 x+74$
• $y^2=73 x^6+10 x^5+59 x^4+85 x^3+29 x^2+107 x+109$
• $y^2=79 x^6+66 x^5+76 x^4+49 x^3+97 x^2+38 x+76$
• $y^2=93 x^6+89 x^5+49 x^4+4 x^3+24 x^2+78 x+51$
• $y^2=54 x^6+65 x^5+88 x^4+68 x^3+110 x^2+34 x+47$
• $y^2=33 x^6+36 x^5+x^4+87 x^3+11 x^2+21 x+17$
• $y^2=79 x^6+48 x^5+84 x^4+68 x^3+81 x^2+11 x+55$
• $y^2=46 x^6+23 x^5+93 x^4+99 x^3+66 x^2+62 x+108$

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 4.0.1040054204.1.

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_ne	$2$	(not in LMFDB)