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:	$32$

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 contains the Jacobians of 32 curves (of which all are hyperelliptic), and hence is principally polarizable:

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

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

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)