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

• Label: 2.167.abs_bfh
• 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:	$1 - 44 x + 813 x^{2} - 7348 x^{3} + 27889 x^{4}$
Frobenius angles:	$\pm0.112931184243$, $\pm0.222892358760$
Angle rank:	$2$ (numerical)
Number field:	4.0.559025.1
Galois group:	$D_{4}$
Jacobians:	$32$
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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$21311$	$769220545$	$21692376200384$	$605001454670128025$	$16872034451782656053431$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$124$	$27580$	$4657552$	$777840468$	$129892805724$	$21691971082990$	$3622557659181172$	$604967117237389668$	$101029508532486547504$	$16871927924972288913900$

Jacobians and polarizations

This isogeny class is principally polarizable and contains the Jacobians of 32 curves (of which all are hyperelliptic):

• $y^2=34 x^6+118 x^5+164 x^4+36 x^3+136 x^2+113 x+135$
• $y^2=140 x^6+4 x^5+136 x^4+133 x^3+88 x^2+12 x+120$
• $y^2=35 x^6+96 x^5+88 x^4+55 x^3+4 x^2+90 x+63$
• $y^2=9 x^6+139 x^5+150 x^4+126 x^3+119 x^2+110 x+119$
• $y^2=102 x^6+107 x^5+23 x^4+109 x^3+15 x^2+42 x+39$
• $y^2=165 x^6+45 x^5+48 x^4+99 x^3+16 x^2+34 x+39$
• $y^2=55 x^6+47 x^5+141 x^4+155 x^3+156 x^2+109 x+52$
• $y^2=27 x^6+56 x^5+39 x^4+96 x^3+162 x^2+141 x+110$
• $y^2=29 x^6+80 x^5+72 x^4+128 x^3+153 x^2+147 x+111$
• $y^2=100 x^6+58 x^5+96 x^4+131 x^3+126 x^2+60 x+32$
• $y^2=x^6+114 x^5+81 x^4+30 x^3+38 x^2+125 x+25$
• $y^2=8 x^6+71 x^5+125 x^4+113 x^3+110 x^2+74 x+41$
• $y^2=110 x^6+142 x^5+160 x^4+140 x^3+8 x^2+92 x+119$
• $y^2=63 x^6+26 x^5+42 x^4+76 x^3+23 x^2+80 x+136$
• $y^2=57 x^6+10 x^5+109 x^4+41 x^3+156 x^2+139 x+14$
• $y^2=145 x^6+101 x^5+143 x^4+18 x^3+69 x^2+32 x+62$
• $y^2=149 x^6+82 x^5+43 x^4+162 x^3+68 x^2+153 x+89$
• $y^2=3 x^6+26 x^5+107 x^4+89 x^3+118 x^2+63 x+73$
• $y^2=32 x^6+148 x^5+115 x^4+74 x^3+53 x^2+99 x+109$
• $y^2=153 x^6+61 x^5+114 x^4+139 x^3+59 x^2+111 x+129$
• and

• $y^2=94 x^6+125 x^5+69 x^4+73 x^3+12 x^2+98 x+67$
• $y^2=146 x^6+166 x^5+90 x^4+12 x^3+107 x^2+113 x+125$
• $y^2=110 x^6+111 x^5+39 x^4+12 x^3+74 x^2+142 x+125$
• $y^2=144 x^6+28 x^5+42 x^4+73 x^3+139 x^2+146 x+148$
• $y^2=159 x^6+128 x^5+25 x^4+115 x^3+87 x^2+42 x+82$
• $y^2=73 x^6+144 x^5+136 x^4+130 x^3+63 x^2+x+138$
• $y^2=111 x^6+95 x^5+30 x^4+150 x^3+22 x^2+29 x+23$
• $y^2=151 x^6+151 x^5+4 x^4+57 x^3+5 x^2+13 x+59$
• $y^2=39 x^6+3 x^5+4 x^4+13 x^3+121 x^2+144 x+141$
• $y^2=91 x^6+84 x^5+21 x^4+87 x^3+89 x^2+92 x+42$
• $y^2=150 x^6+43 x^5+44 x^4+133 x^3+15 x^2+151 x+149$
• $y^2=136 x^6+68 x^5+29 x^4+117 x^3+122 x^2+163 x+35$

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 4.0.559025.1.

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_bfh	$2$	(not in LMFDB)