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

• Label: 2.113.ax_lx
• 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:	$1 - 23 x + 309 x^{2} - 2599 x^{3} + 12769 x^{4}$
Frobenius angles:	$\pm0.163468248542$, $\pm0.432385521597$
Angle rank:	$2$ (numerical)
Number field:	4.0.1828563653.1
Galois group:	$D_{4}$
Jacobians:	$64$

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$10457$	$164185357$	$2083912547489$	$26583628285635029$	$339456571166019388672$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$91$	$12859$	$1444255$	$163042371$	$18424342686$	$2081955475747$	$235260606192199$	$26584442156063139$	$3004041935030433451$	$339456738957725786334$

Jacobians and polarizations

This isogeny class is principally polarizable and contains the Jacobians of 64 curves (of which all are hyperelliptic):

• $y^2=65 x^6+23 x^5+53 x^4+43 x^3+102 x+65$
• $y^2=95 x^6+16 x^5+101 x^4+70 x^3+14 x^2+37 x+110$
• $y^2=19 x^6+92 x^5+94 x^4+75 x^3+33 x^2+35 x+17$
• $y^2=16 x^6+67 x^5+24 x^4+104 x^3+64 x^2+54 x+37$
• $y^2=29 x^6+37 x^5+27 x^4+49 x^3+51 x^2+36 x+59$
• $y^2=2 x^6+92 x^5+95 x^4+85 x^3+69 x^2+38 x+63$
• $y^2=30 x^6+93 x^5+101 x^4+75 x^3+66 x^2+72 x+72$
• $y^2=44 x^6+69 x^5+71 x^4+101 x^3+30 x^2+38 x+40$
• $y^2=24 x^6+64 x^5+x^4+92 x^3+52 x^2+34 x+55$
• $y^2=33 x^6+6 x^5+43 x^4+50 x^3+67 x^2+110 x+72$
• $y^2=100 x^6+65 x^5+58 x^4+45 x^3+89 x^2+87 x+20$
• $y^2=96 x^6+46 x^5+86 x^4+4 x^3+111 x^2+21 x+62$
• $y^2=54 x^6+4 x^5+61 x^4+66 x^3+39 x^2+62 x+95$
• $y^2=37 x^6+75 x^5+6 x^4+55 x^3+101 x^2+37 x+29$
• $y^2=83 x^6+6 x^5+35 x^4+32 x^3+84 x^2+95 x+10$
• $y^2=101 x^6+40 x^5+41 x^4+50 x^3+87 x^2+82 x+84$
• $y^2=67 x^6+13 x^5+109 x^4+68 x^3+46 x^2+99 x+80$
• $y^2=57 x^6+41 x^5+18 x^4+66 x^3+58 x^2+61 x+93$
• $y^2=63 x^6+50 x^5+79 x^4+94 x^3+63 x^2+107$
• $y^2=73 x^6+25 x^5+5 x^4+23 x^3+11 x^2+18 x+27$
• and

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

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 4.0.1828563653.1.

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_lx	$2$	(not in LMFDB)