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

• Label: 2.113.ay_lo
• 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:	$1 - 24 x + 300 x^{2} - 2712 x^{3} + 12769 x^{4}$
Frobenius angles:	$\pm0.0926205767236$, $\pm0.445332252509$
Angle rank:	$2$ (numerical)
Number field:	4.0.1279801600.1
Galois group:	$D_{4}$
Jacobians:	$48$

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$10334$	$163339204$	$2081433367694$	$26579575164869776$	$339452374232886007214$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$90$	$12794$	$1442538$	$163017510$	$18424114890$	$2081953739738$	$235260590445306$	$26584442089234174$	$3004041937522316634$	$339456739022701005914$

Jacobians and polarizations

This isogeny class is principally polarizable and contains the Jacobians of 48 curves (of which all are hyperelliptic):

• $y^2=64 x^6+10 x^5+11 x^4+65 x^3+46 x^2+65 x+42$
• $y^2=32 x^6+73 x^5+31 x^4+22 x^3+16 x^2+49 x+103$
• $y^2=106 x^6+3 x^5+94 x^4+104 x^3+30 x^2+31 x+45$
• $y^2=29 x^6+99 x^5+49 x^4+95 x^3+22 x^2+31 x+87$
• $y^2=85 x^6+64 x^5+46 x^4+79 x^3+35 x^2+81 x+26$
• $y^2=4 x^6+49 x^5+17 x^4+60 x^3+33 x^2+50 x+35$
• $y^2=93 x^6+106 x^5+78 x^4+46 x^3+95 x^2+64 x+107$
• $y^2=46 x^6+4 x^5+49 x^4+31 x^3+86 x^2+94 x+102$
• $y^2=19 x^6+72 x^5+78 x^4+66 x^3+105 x^2+16 x+20$
• $y^2=x^6+110 x^5+57 x^4+16 x^3+68 x^2+83 x+59$
• $y^2=4 x^6+59 x^5+8 x^4+28 x^3+90 x^2+6 x+58$
• $y^2=102 x^6+3 x^5+91 x^4+82 x^3+106 x^2+76 x+7$
• $y^2=82 x^6+18 x^5+54 x^4+90 x^3+98 x^2+87 x+45$
• $y^2=52 x^6+99 x^5+78 x^4+55 x^2+58 x+75$
• $y^2=31 x^6+50 x^5+68 x^4+88 x^3+103 x^2+32 x+109$
• $y^2=49 x^6+58 x^5+61 x^4+41 x^3+18 x^2+15 x+102$
• $y^2=22 x^6+103 x^5+101 x^4+111 x^3+99 x^2+32 x+94$
• $y^2=56 x^6+50 x^5+78 x^4+74 x^3+5 x^2+46 x+8$
• $y^2=5 x^6+75 x^5+87 x^4+17 x^3+3 x^2+54 x+90$
• $y^2=68 x^6+3 x^5+40 x^4+3 x^3+29 x^2+100 x+64$
• and

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

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 4.0.1279801600.1.

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.y_lo	$2$	(not in LMFDB)