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

• Label: 2.113.ax_kk
• 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:	$1 - 23 x + 270 x^{2} - 2599 x^{3} + 12769 x^{4}$
Frobenius angles:	$\pm0.0591605281587$, $\pm0.468419306862$
Angle rank:	$2$ (numerical)
Number field:	4.0.860798972.1
Galois group:	$D_{4}$
Jacobians:	$44$

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$10418$	$163166716$	$2080028376224$	$26577537153031616$	$339451365348344385298$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$91$	$12781$	$1441564$	$163005009$	$18424060131$	$2081952872146$	$235260559501555$	$26584441673067873$	$3004041935636949868$	$339456739022833737021$

Jacobians and polarizations

This isogeny class is principally polarizable and contains the Jacobians of 44 curves (of which all are hyperelliptic):

• $y^2=109 x^6+63 x^4+89 x^3+105 x^2+12 x+103$
• $y^2=102 x^6+44 x^5+108 x^4+71 x^3+107 x^2+102 x+3$
• $y^2=31 x^6+22 x^5+4 x^4+83 x^3+51 x^2+103 x+78$
• $y^2=43 x^6+44 x^5+24 x^4+111 x^3+38 x^2+32 x+59$
• $y^2=78 x^6+31 x^5+59 x^4+96 x^3+102 x^2+4 x+84$
• $y^2=43 x^6+94 x^5+90 x^4+47 x^3+73 x^2+56 x+83$
• $y^2=102 x^6+24 x^5+54 x^4+9 x^3+15 x^2+97 x+11$
• $y^2=71 x^6+85 x^5+27 x^4+22 x^3+68 x+37$
• $y^2=50 x^6+110 x^5+87 x^4+68 x^3+75 x^2+2 x+21$
• $y^2=16 x^6+17 x^5+52 x^4+33 x^3+44 x^2+92 x+51$
• $y^2=74 x^6+82 x^5+63 x^4+77 x^3+91 x^2+106 x+39$
• $y^2=16 x^6+23 x^5+19 x^4+14 x^3+6 x^2+39 x+13$
• $y^2=29 x^6+3 x^5+46 x^4+112 x^3+102 x^2+22 x+29$
• $y^2=84 x^6+55 x^5+22 x^4+13 x^3+51 x^2+x+47$
• $y^2=106 x^6+77 x^5+100 x^4+69 x^3+72 x^2+100 x+29$
• $y^2=55 x^6+69 x^5+100 x^4+49 x^3+77 x^2+32 x+40$
• $y^2=69 x^6+15 x^5+39 x^4+94 x^3+13 x^2+79 x+33$
• $y^2=73 x^6+11 x^5+38 x^4+79 x^3+64 x^2+110 x+99$
• $y^2=39 x^6+99 x^5+36 x^4+49 x^3+69 x^2+56 x+87$
• $y^2=75 x^6+67 x^5+86 x^4+34 x^3+64 x^2+35 x+99$
• and

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

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 4.0.860798972.1.

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.x_kk	$2$	(not in LMFDB)