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

• Label: 2.113.ay_ln
• 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:	$1 - 24 x + 299 x^{2} - 2712 x^{3} + 12769 x^{4}$
Frobenius angles:	$\pm0.0894603824394$, $\pm0.446236920729$
Angle rank:	$2$ (numerical)
Number field:	4.0.1231859088.1
Galois group:	$D_{4}$
Jacobians:	$52$

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$10333$	$163313065$	$2081329443508$	$26579394854732025$	$339452175252514669573$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$90$	$12792$	$1442466$	$163016404$	$18424104090$	$2081953611654$	$235260588283482$	$26584442062467556$	$3004041937359245058$	$339456739022723314632$

Jacobians and polarizations

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

• $y^2=106 x^6+55 x^5+95 x^4+35 x^3+103 x^2+44 x+9$
• $y^2=47 x^6+26 x^5+2 x^4+111 x^3+94 x^2+102 x+10$
• $y^2=42 x^6+76 x^5+79 x^4+57 x^3+30 x^2+111 x+92$
• $y^2=50 x^6+89 x^5+61 x^4+11 x^3+2 x^2+19 x+29$
• $y^2=50 x^6+53 x^5+59 x^4+102 x^3+99 x^2+34 x+47$
• $y^2=70 x^6+24 x^5+83 x^4+22 x^3+64 x^2+79 x+87$
• $y^2=30 x^6+55 x^5+93 x^4+72 x^3+61 x^2+64 x+10$
• $y^2=72 x^6+33 x^5+4 x^4+69 x^3+102 x^2+34 x+8$
• $y^2=14 x^6+88 x^5+74 x^4+58 x^3+5 x^2+78 x+86$
• $y^2=16 x^6+101 x^5+41 x^4+12 x^3+43 x^2+25 x+111$
• $y^2=99 x^6+54 x^5+97 x^4+67 x^3+81 x^2+6 x+110$
• $y^2=78 x^6+20 x^5+108 x^4+95 x^3+66 x^2+26 x+106$
• $y^2=71 x^6+106 x^5+21 x^4+101 x^3+76 x^2+103 x+19$
• $y^2=67 x^6+48 x^5+44 x^4+8 x^3+99 x^2+81 x+92$
• $y^2=74 x^6+65 x^5+36 x^4+87 x^3+106 x^2+38 x+8$
• $y^2=57 x^6+101 x^5+93 x^4+71 x^3+29 x^2+35 x+5$
• $y^2=38 x^6+69 x^5+82 x^4+78 x^3+54 x^2+15 x+111$
• $y^2=46 x^6+59 x^5+48 x^4+86 x^3+37 x^2+72 x+45$
• $y^2=67 x^6+89 x^5+14 x^4+4 x^3+77 x^2+37 x+81$
• $y^2=40 x^6+37 x^5+88 x^4+108 x^3+80 x^2+32 x+76$
• and

• $y^2=56 x^6+103 x^5+109 x^4+47 x^3+13 x^2+59 x+88$
• $y^2=23 x^6+103 x^5+110 x^4+3 x^3+24 x^2+35 x+85$
• $y^2=33 x^6+79 x^5+109 x^4+108 x^3+94 x^2+97 x+52$
• $y^2=45 x^6+25 x^5+71 x^4+16 x^3+69 x^2+79 x+76$
• $y^2=54 x^6+36 x^5+102 x^4+74 x^3+77 x^2+31 x+33$
• $y^2=100 x^6+42 x^5+102 x^4+x^3+70 x^2+64 x+78$
• $y^2=25 x^6+93 x^5+93 x^4+63 x^3+78 x^2+90 x+86$
• $y^2=74 x^6+30 x^5+66 x^4+32 x^3+42 x^2+96 x+73$
• $y^2=94 x^6+104 x^5+54 x^4+29 x^3+68 x^2+81 x+90$
• $y^2=27 x^6+6 x^5+56 x^4+x^3+80 x^2+40 x+6$
• $y^2=108 x^6+50 x^5+110 x^4+98 x^3+19 x^2+58 x+35$
• $y^2=3 x^6+42 x^5+69 x^4+58 x^3+60 x^2+22 x+66$
• $y^2=53 x^6+102 x^5+107 x^4+49 x^3+104 x^2+52 x+47$
• $y^2=110 x^6+21 x^5+90 x^4+35 x^3+100 x^2+52 x+14$
• $y^2=48 x^6+77 x^5+41 x^4+72 x^3+59 x^2+8 x+19$
• $y^2=11 x^6+104 x^5+34 x^4+5 x^3+105 x^2+103 x+66$
• $y^2=110 x^6+103 x^5+37 x^4+40 x^3+49 x^2+102 x+61$
• $y^2=110 x^6+71 x^5+96 x^4+22 x^3+90 x^2+92 x+65$
• $y^2=94 x^6+104 x^5+52 x^4+72 x^3+104 x^2+105 x+8$
• $y^2=93 x^6+103 x^5+95 x^4+17 x^3+74 x^2+99 x+59$
• $y^2=90 x^6+18 x^5+66 x^4+75 x^3+58 x^2+83 x+107$
• $y^2=83 x^6+107 x^5+22 x^4+x^3+16 x^2+103 x+27$
• $y^2=5 x^6+110 x^5+30 x^4+43 x^3+23 x^2+34 x+54$
• $y^2=110 x^6+22 x^5+97 x^4+54 x^3+32 x^2+84 x+30$
• $y^2=80 x^6+35 x^5+74 x^4+71 x^3+38 x^2+46 x+4$
• $y^2=35 x^6+50 x^5+32 x^4+72 x^3+69 x^2+95 x+7$
• $y^2=58 x^6+78 x^5+108 x^4+34 x^3+41 x^2+x+96$
• $y^2=10 x^6+29 x^5+89 x^4+48 x^3+61 x^2+108 x+82$
• $y^2=39 x^6+106 x^5+80 x^4+107 x^3+29 x^2+29 x+4$
• $y^2=112 x^6+91 x^5+49 x^4+18 x^3+109 x^2+66 x+92$
• $y^2=86 x^6+93 x^5+20 x^4+20 x^3+51 x^2+3 x+51$
• $y^2=22 x^6+95 x^5+20 x^4+88 x^3+25 x^2+95 x+77$

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 4.0.1231859088.1.

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_ln	$2$	(not in LMFDB)