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

• Label: 2.113.ay_le
• 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:	$1 - 24 x + 290 x^{2} - 2712 x^{3} + 12769 x^{4}$
Frobenius angles:	$\pm0.0549511815408$, $\pm0.454090521595$
Angle rank:	$2$ (numerical)
Number field:	4.0.147600.1
Galois group:	$D_{4}$
Jacobians:	$120$

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$10324$	$163077904$	$2080394205844$	$26577742734360576$	$339450185445069897364$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$90$	$12774$	$1441818$	$163006270$	$18423996090$	$2081952152358$	$235260563141946$	$26584441735502974$	$3004041934586729754$	$339456739002653210214$

Jacobians and polarizations

This isogeny class is principally polarizable and contains the Jacobians of 120 curves (of which all are hyperelliptic):

• $y^2=85 x^6+39 x^5+97 x^4+84 x^3+85 x^2+51 x+66$
• $y^2=33 x^6+95 x^5+59 x^4+90 x^3+12 x^2+17$
• $y^2=36 x^6+35 x^5+42 x^4+80 x^3+13 x^2+83 x+37$
• $y^2=29 x^6+79 x^5+11 x^4+77 x^3+70 x^2+15 x+75$
• $y^2=112 x^6+36 x^5+50 x^4+55 x^3+87 x^2+54 x+52$
• $y^2=33 x^6+4 x^5+57 x^4+39 x^3+31 x^2+23 x+28$
• $y^2=65 x^6+68 x^5+25 x^4+90 x^3+78 x^2+9 x+6$
• $y^2=99 x^6+55 x^5+38 x^4+77 x^3+53 x^2+27 x+86$
• $y^2=59 x^6+82 x^5+62 x^4+112 x^3+93 x^2+30 x+100$
• $y^2=95 x^6+91 x^5+61 x^4+71 x^3+57 x^2+37 x+110$
• $y^2=45 x^6+75 x^5+32 x^4+13 x^3+3 x^2+33 x+80$
• $y^2=70 x^6+43 x^5+44 x^4+38 x^3+111 x^2+43 x+33$
• $y^2=19 x^6+33 x^5+82 x^4+98 x^3+20 x^2+40 x+93$
• $y^2=75 x^5+16 x^4+76 x^3+30 x^2+44 x+48$
• $y^2=67 x^6+69 x^5+60 x^4+6 x^3+84 x^2+24 x+40$
• $y^2=39 x^6+18 x^5+75 x^4+16 x^3+31 x^2+43 x+60$
• $y^2=71 x^6+53 x^5+76 x^4+56 x^3+43 x^2+11 x+10$
• $y^2=2 x^6+19 x^5+56 x^4+112 x^3+84 x^2+63 x+90$
• $y^2=112 x^6+46 x^4+77 x^3+41 x^2+10 x+15$
• $y^2=89 x^6+91 x^5+72 x^4+52 x^3+63 x^2+96 x+74$
• and

• $y^2=37 x^6+109 x^4+22 x^3+109 x^2+3 x+27$
• $y^2=28 x^6+94 x^5+75 x^4+59 x^3+6 x^2+98 x+25$
• $y^2=14 x^6+109 x^5+38 x^4+19 x^3+8 x^2+5 x$
• $y^2=3 x^6+61 x^5+90 x^4+36 x^3+76 x^2+35 x+25$
• $y^2=86 x^6+41 x^5+65 x^4+29 x^3+56 x^2+76 x+89$
• $y^2=39 x^6+39 x^5+100 x^4+104 x^3+81 x^2+13 x+47$
• $y^2=51 x^6+54 x^5+3 x^4+65 x^3+89 x^2+85 x+50$
• $y^2=101 x^6+80 x^5+19 x^4+48 x^3+73 x^2+75 x+43$
• $y^2=66 x^6+110 x^5+35 x^4+95 x^3+63 x^2+15 x+24$
• $y^2=110 x^6+49 x^5+33 x^4+36 x^3+88 x^2+21 x+36$
• $y^2=96 x^6+11 x^5+17 x^4+4 x^3+49 x^2+79 x+88$
• $y^2=80 x^6+93 x^5+14 x^4+56 x^3+14 x^2+106 x+11$
• $y^2=39 x^6+89 x^5+71 x^4+45 x^3+97 x^2+7 x+58$
• $y^2=32 x^6+57 x^5+9 x^4+74 x^3+28 x^2+96 x+83$
• $y^2=14 x^6+80 x^5+39 x^4+74 x^3+110 x^2+106 x+110$
• $y^2=67 x^6+31 x^5+16 x^4+35 x^3+23 x^2+105 x+68$
• $y^2=2 x^6+96 x^5+82 x^4+79 x^3+48 x^2+91 x+29$
• $y^2=94 x^6+88 x^5+106 x^4+72 x^3+35 x^2+90 x+9$
• $y^2=53 x^6+52 x^5+102 x^4+99 x^3+52 x^2+81 x+106$
• $y^2=52 x^6+64 x^5+9 x^4+96 x^3+43 x^2+110 x+27$
• $y^2=26 x^6+23 x^5+104 x^4+49 x^3+46 x^2+43 x+100$
• $y^2=10 x^6+29 x^5+112 x^4+70 x^3+47 x^2+22 x+58$
• $y^2=92 x^6+54 x^5+15 x^4+3 x^3+10 x^2+71 x+99$
• $y^2=35 x^6+97 x^5+9 x^4+86 x^3+32 x^2+49 x+42$
• $y^2=76 x^6+70 x^5+96 x^4+89 x^3+3 x^2+41 x+70$
• $y^2=43 x^6+112 x^5+5 x^4+94 x^3+46 x^2+68 x+107$
• $y^2=70 x^6+91 x^5+31 x^4+42 x^3+104 x^2+110 x+75$
• $y^2=72 x^6+x^5+62 x^4+52 x^3+58 x^2+76 x+74$
• $y^2=74 x^6+32 x^5+34 x^4+4 x^3+107 x^2+15 x+25$
• $y^2=43 x^6+72 x^5+61 x^4+110 x^3+104 x^2+12 x+7$
• $y^2=88 x^6+92 x^5+67 x^4+47 x^3+38 x^2+9 x+24$
• $y^2=112 x^6+16 x^4+27 x^3+60 x^2+112 x+49$
• $y^2=20 x^6+100 x^5+71 x^4+8 x^3+43 x^2+11 x$
• $y^2=112 x^6+92 x^5+36 x^4+89 x^3+61 x^2+93 x+53$
• $y^2=35 x^6+72 x^5+56 x^4+35 x^3+90 x^2+x+37$
• $y^2=23 x^6+39 x^5+58 x^4+14 x^3+26 x^2+95 x+37$
• $y^2=11 x^6+90 x^5+83 x^4+9 x^3+19 x^2+110 x+65$
• $y^2=55 x^6+111 x^5+71 x^4+46 x^3+74 x^2+5 x+103$
• $y^2=x^6+26 x^5+19 x^4+96 x^3+57 x^2+42 x+96$
• $y^2=90 x^6+93 x^5+59 x^4+95 x^3+55 x^2+82 x+27$
• $y^2=6 x^6+51 x^5+90 x^4+42 x^3+63 x^2+89 x+45$
• $y^2=22 x^6+69 x^5+82 x^4+42 x^3+66 x^2+110 x+38$
• $y^2=71 x^6+30 x^5+86 x^4+25 x^3+72 x^2+72 x+85$
• $y^2=94 x^6+79 x^5+79 x^4+29 x^3+60 x+60$
• $y^2=5 x^6+45 x^5+11 x^4+12 x^3+73 x^2+3 x+111$
• $y^2=109 x^6+105 x^5+101 x^4+112 x^3+17 x^2+6 x+50$
• $y^2=32 x^6+47 x^5+87 x^4+9 x^3+42 x^2+108 x+92$
• $y^2=23 x^6+86 x^5+12 x^4+92 x^3+13 x^2+48 x+104$
• $y^2=30 x^6+25 x^5+107 x^4+112 x^3+108 x^2+99 x+23$
• $y^2=33 x^6+90 x^5+69 x^4+69 x^3+69 x^2+44 x+95$
• $y^2=40 x^6+75 x^5+84 x^4+92 x^3+63 x^2+3 x+54$
• $y^2=87 x^6+77 x^5+66 x^4+44 x^3+11 x^2+112 x+94$
• $y^2=15 x^6+108 x^5+52 x^4+109 x^3+85 x^2+34 x+72$
• $y^2=75 x^6+34 x^5+42 x^4+14 x^3+72 x^2+61 x+110$
• $y^2=35 x^6+104 x^5+108 x^4+104 x^3+35 x^2+3 x+55$
• $y^2=63 x^6+63 x^5+4 x^4+112 x^3+40 x^2+17 x+106$
• $y^2=59 x^6+99 x^5+110 x^4+69 x^3+32 x^2+65 x+61$
• $y^2=94 x^6+36 x^5+27 x^4+x^3+64 x^2+79 x+96$
• $y^2=47 x^6+80 x^5+19 x^4+12 x^3+55 x^2+32 x+14$
• $y^2=52 x^6+111 x^5+112 x^4+26 x^3+101 x^2+66 x+12$
• $y^2=37 x^6+10 x^4+26 x^3+108 x^2+88 x+66$
• $y^2=79 x^6+49 x^5+89 x^4+75 x^3+69 x^2+44 x+74$
• $y^2=97 x^6+18 x^5+54 x^4+38 x^3+40 x^2+60 x+23$
• $y^2=92 x^6+71 x^5+41 x^4+25 x^3+46 x^2+94 x+11$
• $y^2=60 x^6+62 x^5+66 x^4+65 x^3+33 x^2+99 x+92$
• $y^2=63 x^6+68 x^5+40 x^4+25 x^3+5 x^2+22 x+45$
• $y^2=67 x^6+102 x^5+93 x^4+88 x^3+11 x^2+33 x+33$
• $y^2=67 x^6+94 x^4+87 x^3+6 x^2+61 x+8$
• $y^2=3 x^6+97 x^5+86 x^4+44 x^3+41 x^2+x+102$
• $y^2=43 x^6+97 x^5+37 x^4+91 x^3+74 x^2+54 x+23$
• $y^2=34 x^6+69 x^5+24 x^4+67 x^3+56 x+43$
• $y^2=25 x^6+97 x^5+96 x^4+88 x^3+49 x^2+36 x+67$
• $y^2=107 x^6+89 x^5+110 x^4+88 x^3+102 x^2+70 x+73$
• $y^2=78 x^6+68 x^5+2 x^4+66 x^3+58 x^2+95 x+29$
• $y^2=63 x^6+69 x^5+104 x^4+73 x^3+73 x^2+16 x+108$
• $y^2=59 x^6+51 x^5+80 x^4+70 x^3+43 x^2+47 x+24$
• $y^2=71 x^6+11 x^5+12 x^4+42 x^3+111 x^2+111 x+45$
• $y^2=35 x^6+83 x^5+26 x^4+16 x^3+16 x^2+22 x+84$
• $y^2=71 x^6+51 x^5+97 x^4+85 x^3+40 x^2+19 x+6$
• $y^2=65 x^6+34 x^5+7 x^4+12 x^3+41 x^2+33 x+24$
• $y^2=90 x^6+67 x^5+96 x^4+86 x^3+10 x^2+86 x+58$
• $y^2=63 x^6+53 x^5+108 x^4+61 x^3+25 x^2+7 x+74$
• $y^2=18 x^5+47 x^4+68 x^3+109 x^2+73 x+71$
• $y^2=66 x^6+99 x^5+38 x^4+29 x^3+23 x^2+41 x+12$
• $y^2=3 x^6+25 x^5+81 x^4+29 x^3+75 x^2+46 x+73$
• $y^2=27 x^6+19 x^5+64 x^4+112 x^3+69 x^2+32 x+30$
• $y^2=100 x^6+57 x^5+97 x^4+97 x^3+31 x^2+97 x+53$
• $y^2=67 x^6+x^5+53 x^4+106 x^3+4 x^2+48 x+6$
• $y^2=105 x^6+11 x^4+41 x^3+96 x^2+19 x+58$
• $y^2=78 x^6+63 x^5+88 x^4+36 x^3+110 x^2+4 x+70$
• $y^2=24 x^6+3 x^5+97 x^4+18 x^3+79 x^2+94 x+8$
• $y^2=92 x^6+4 x^5+99 x^4+53 x^3+68 x^2+43 x+81$
• $y^2=91 x^6+90 x^5+93 x^4+38 x^3+106 x^2+27 x+94$
• $y^2=45 x^6+69 x^5+34 x^4+94 x^3+68 x^2+60 x+71$
• $y^2=68 x^6+92 x^5+23 x^4+36 x^3+99 x^2+49 x+58$
• $y^2=109 x^6+73 x^5+74 x^4+45 x^3+101 x^2+106 x+37$
• $y^2=47 x^6+98 x^5+x^4+109 x^3+91 x^2+21 x+106$
• $y^2=108 x^6+57 x^5+89 x^4+30 x^3+18 x^2+33 x+108$
• $y^2=x^6+54 x^5+100 x^4+32 x^3+105 x^2+103 x+70$
• $y^2=94 x^6+39 x^5+42 x^4+99 x^3+15 x^2+95 x+73$

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 4.0.147600.1.

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_le	$2$	(not in LMFDB)