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

• Label: 2.113.ax_lu
• 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:	$1 - 23 x + 306 x^{2} - 2599 x^{3} + 12769 x^{4}$
Frobenius angles:	$\pm0.156931090073$, $\pm0.435607389426$
Angle rank:	$2$ (numerical)
Number field:	4.0.1918294796.1
Galois group:	$D_{4}$
Jacobians:	$50$

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$10454$	$164106892$	$2083613669504$	$26583194930100224$	$339456399548528977174$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$91$	$12853$	$1444048$	$163039713$	$18424333371$	$2081955598498$	$235260607573579$	$26584442171172801$	$3004041935567668624$	$339456738968162434293$

Jacobians and polarizations

This isogeny class is principally polarizable and contains the Jacobians of 50 curves (of which all are hyperelliptic):

• $y^2=54 x^6+94 x^5+46 x^4+104 x^3+19 x^2+82 x+16$
• $y^2=8 x^6+83 x^5+30 x^4+44 x^3+23 x^2+28 x+102$
• $y^2=84 x^6+31 x^5+43 x^4+16 x^3+57 x^2+112 x+35$
• $y^2=59 x^6+104 x^5+16 x^4+90 x^3+36 x^2+98 x+26$
• $y^2=56 x^6+91 x^5+87 x^4+104 x^3+20 x^2+86 x+34$
• $y^2=59 x^6+39 x^5+106 x^4+35 x^3+37 x^2+32 x+89$
• $y^2=94 x^6+91 x^5+81 x^4+13 x^3+39 x^2+3 x+101$
• $y^2=59 x^6+11 x^5+57 x^4+22 x^3+86 x^2+6 x+86$
• $y^2=37 x^6+102 x^5+15 x^4+105 x^3+105 x^2+112 x+86$
• $y^2=12 x^6+73 x^5+87 x^4+87 x^3+81 x^2+79 x+22$
• $y^2=95 x^6+76 x^5+97 x^4+58 x^3+58 x^2+96 x+106$
• $y^2=93 x^6+34 x^5+42 x^4+70 x^3+21 x^2+12 x+90$
• $y^2=43 x^6+79 x^4+23 x^3+13 x^2+70 x+92$
• $y^2=101 x^6+80 x^5+79 x^4+94 x^3+36 x^2+31 x+97$
• $y^2=97 x^6+24 x^5+92 x^4+18 x^3+55 x^2+4 x+27$
• $y^2=32 x^6+52 x^5+29 x^4+47 x^3+102 x^2+48 x+26$
• $y^2=7 x^6+46 x^5+38 x^4+61 x^3+76 x^2+33 x+22$
• $y^2=54 x^6+27 x^5+87 x^4+85 x^3+65 x^2+12 x+61$
• $y^2=72 x^6+93 x^5+5 x^4+71 x^3+86 x^2+106 x+10$
• $y^2=17 x^6+6 x^5+71 x^4+54 x^3+62 x^2+101 x+45$
• and

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

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 4.0.1918294796.1.

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_lu	$2$	(not in LMFDB)