Abelian variety isogeny class 2.167.abs_bez over $\F_{167}$

• Label: 2.167.abs_bez
• Base field: $\F_{167}$
• 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:	$\F_{167}$
Dimension:	$2$
L-polynomial:	$1 - 44 x + 805 x^{2} - 7348 x^{3} + 27889 x^{4}$
Frobenius angles:	$\pm0.0434254521130$, $\pm0.247924377782$
Angle rank:	$2$ (numerical)
Number field:	4.0.688337.1
Galois group:	$D_{4}$
Jacobians:	$34$
Cyclic group of points:	yes

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$21303$	$768761361$	$21687450639552$	$604973402008177401$	$16871923575591307449183$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$124$	$27564$	$4656496$	$777804404$	$129891952124$	$21691955596014$	$3622557435915668$	$604967114690152228$	$101029508510725282000$	$16871927924858890758204$

Jacobians and polarizations

This isogeny class is principally polarizable and contains the Jacobians of 34 curves (of which all are hyperelliptic):

• $y^2=78 x^6+153 x^5+123 x^4+145 x^3+52 x^2+164 x+26$
• $y^2=110 x^6+155 x^5+146 x^4+132 x^3+87 x^2+55 x+117$
• $y^2=93 x^6+123 x^5+122 x^4+66 x^3+28 x^2+62 x+30$
• $y^2=104 x^6+37 x^5+50 x^4+5 x^3+77 x+128$
• $y^2=60 x^6+159 x^5+119 x^4+40 x^3+139 x^2+92 x+107$
• $y^2=56 x^6+34 x^5+141 x^4+139 x^3+134 x^2+24 x+132$
• $y^2=47 x^6+117 x^5+126 x^4+81 x^3+16 x^2+45 x+67$
• $y^2=144 x^6+112 x^5+63 x^4+160 x^3+108 x^2+61 x+45$
• $y^2=24 x^6+150 x^5+135 x^4+85 x^3+58 x^2+32 x+31$
• $y^2=4 x^6+141 x^5+15 x^4+139 x^3+17 x^2+73 x+84$
• $y^2=2 x^6+15 x^5+163 x^4+162 x^3+141 x^2+102 x+63$
• $y^2=91 x^6+73 x^5+64 x^4+77 x^3+122 x^2+38 x+46$
• $y^2=85 x^6+51 x^5+77 x^4+125 x^3+5 x^2+31 x+120$
• $y^2=103 x^6+19 x^5+110 x^4+88 x^3+118 x^2+85 x+80$
• $y^2=129 x^6+127 x^5+43 x^4+123 x^3+156 x^2+162 x+121$
• $y^2=28 x^6+69 x^5+8 x^4+64 x^3+149 x^2+131 x+43$
• $y^2=16 x^6+153 x^5+30 x^4+11 x^3+100 x^2+48 x+139$
• $y^2=54 x^6+105 x^5+91 x^4+48 x^3+109 x^2+147 x+155$
• $y^2=92 x^6+37 x^5+69 x^4+144 x^3+108 x^2+125 x+128$
• $y^2=35 x^6+121 x^5+68 x^4+105 x^3+11 x^2+107 x+131$
• and

• $y^2=115 x^6+38 x^5+67 x^4+153 x^3+138 x^2+127 x+123$
• $y^2=118 x^6+66 x^5+113 x^4+118 x^3+112 x^2+112 x+55$
• $y^2=52 x^6+129 x^5+18 x^4+46 x^3+35 x^2+119 x+4$
• $y^2=25 x^6+63 x^5+66 x^4+63 x^3+33 x^2+10 x+165$
• $y^2=160 x^6+161 x^5+137 x^4+30 x^3+66 x^2+144 x+63$
• $y^2=60 x^6+82 x^5+125 x^4+144 x^3+19 x^2+29 x+97$
• $y^2=147 x^6+104 x^5+81 x^4+57 x^3+108 x^2+121 x+126$
• $y^2=125 x^6+88 x^5+138 x^4+42 x^3+45 x^2+136 x+70$
• $y^2=40 x^6+44 x^5+28 x^4+84 x^3+89 x^2+136 x+49$
• $y^2=106 x^6+42 x^5+123 x^4+39 x^3+24 x^2+38 x+79$
• $y^2=90 x^6+89 x^5+105 x^4+72 x^3+47 x^2+96 x+24$
• $y^2=32 x^6+146 x^5+137 x^4+8 x^3+38 x^2+3 x+111$
• $y^2=2 x^6+2 x^5+44 x^4+10 x^3+35 x^2+138 x+164$
• $y^2=148 x^6+150 x^5+118 x^4+23 x^3+94 x^2+122 x+40$

Decomposition and endomorphism algebra

All geometric endomorphisms are defined over $\F_{167}$.

Endomorphism algebra over $\F_{167}$

The endomorphism algebra of this simple isogeny class is 4.0.688337.1.

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
2.167.bs_bez	$2$	(not in LMFDB)