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

• Label: 2.113.ax_kl
• 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:	$1 - 23 x + 271 x^{2} - 2599 x^{3} + 12769 x^{4}$
Frobenius angles:	$\pm0.0633394078667$, $\pm0.467616104285$
Angle rank:	$2$ (numerical)
Number field:	4.0.962349701.1
Galois group:	$D_{4}$
Jacobians:	$45$
Isomorphism classes:	45

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$10419$	$163192797$	$2080127938059$	$26577705720223269$	$339451579345745554224$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$91$	$12783$	$1441633$	$163006043$	$18424071746$	$2081953055223$	$235260562662629$	$26584441712023411$	$3004041935992324639$	$339456739026584323518$

Jacobians and polarizations

This isogeny class is principally polarizable and contains the Jacobians of 45 curves (of which all are hyperelliptic):

• $y^2=83 x^6+40 x^5+69 x^4+86 x^3+62 x^2+83 x$
• $y^2=74 x^6+56 x^5+109 x^4+112 x^3+14 x^2+76 x+92$
• $y^2=30 x^6+68 x^5+42 x^4+72 x^3+5 x^2+93 x+29$
• $y^2=56 x^6+21 x^5+49 x^4+67 x^3+86 x^2+52 x+92$
• $y^2=108 x^6+8 x^5+76 x^4+10 x^3+33 x^2+23 x+84$
• $y^2=100 x^6+34 x^5+63 x^4+98 x^3+52 x^2+98 x+58$
• $y^2=71 x^6+73 x^5+34 x^4+109 x^3+3 x^2+81 x+82$
• $y^2=24 x^6+70 x^5+3 x^4+46 x^3+104 x^2+9 x+73$
• $y^2=14 x^6+61 x^5+49 x^4+8 x^3+15 x^2+108 x+12$
• $y^2=16 x^6+112 x^5+99 x^4+101 x^3+4 x^2+105 x+108$
• $y^2=14 x^6+69 x^5+110 x^4+6 x^3+53 x^2+92 x+61$
• $y^2=99 x^6+31 x^5+96 x^4+19 x^3+35 x^2+27 x+35$
• $y^2=4 x^6+81 x^5+73 x^4+83 x^3+85 x^2+39 x+109$
• $y^2=58 x^6+15 x^5+69 x^4+18 x^3+21 x^2+21 x+90$
• $y^2=65 x^6+98 x^5+91 x^4+71 x^3+76 x^2+52 x+70$
• $y^2=13 x^6+19 x^5+72 x^4+73 x^3+26 x^2+9 x+37$
• $y^2=83 x^6+44 x^5+76 x^4+110 x^3+101 x^2+11 x$
• $y^2=7 x^6+57 x^5+70 x^4+9 x^3+6 x^2+99 x+66$
• $y^2=93 x^6+86 x^5+83 x^4+62 x^3+10 x^2+41 x+75$
• $y^2=x^6+17 x^5+89 x^4+2 x^3+19 x^2+56 x+96$
• and

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

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 4.0.962349701.1.

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_kl	$2$	(not in LMFDB)