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

• Label: 2.167.abu_bhd
• 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:	$1 - 46 x + 861 x^{2} - 7682 x^{3} + 27889 x^{4}$
Frobenius angles:	$\pm0.106436151366$, $\pm0.185363903762$
Angle rank:	$2$ (numerical)
Number field:	4.0.930368.1
Galois group:	$D_{4}$
Jacobians:	$9$

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$21023$	$766898017$	$21684684881636$	$604986931605506729$	$16872028538792637715903$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$122$	$27496$	$4655900$	$777821796$	$129892760202$	$21691974268198$	$3622557741881942$	$604967118433940484$	$101029508542297691012$	$16871927924950784322216$

Jacobians and polarizations

This isogeny class contains the Jacobians of 9 curves (of which all are hyperelliptic), and hence is principally polarizable:

• $y^2=109x^6+99x^5+53x^3+104x^2+159x+133$
• $y^2=106x^6+77x^5+155x^4+117x^3+145x^2+41x+140$
• $y^2=86x^6+162x^5+54x^4+77x^3+154x^2+45x+123$
• $y^2=139x^6+68x^5+4x^4+94x^3+128x^2+52x+10$
• $y^2=116x^6+106x^5+115x^4+18x^3+162x^2+50x+144$
• $y^2=126x^6+118x^5+75x^4+146x^3+49x^2+153x+47$
• $y^2=26x^6+68x^5+126x^4+76x^3+3x^2+42x+85$
• $y^2=56x^6+16x^5+74x^4+12x^3+118x^2+56x+140$
• $y^2=75x^6+129x^5+91x^4+137x^3+91x^2+78x+30$

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 4.0.930368.1.

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.bu_bhd	$2$	(not in LMFDB)