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

• Label: 2.167.abt_bgh
• 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:	$1 - 45 x + 839 x^{2} - 7515 x^{3} + 27889 x^{4}$
Frobenius angles:	$\pm0.133126802687$, $\pm0.189879610789$
Angle rank:	$2$ (numerical)
Number field:	4.0.580725.2
Galois group:	$D_{4}$
Jacobians:	$12$

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$21169$	$768201841$	$21690083381431$	$605003122161559341$	$16872066922857743852464$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$123$	$27543$	$4657059$	$777842611$	$129893055708$	$21691977548307$	$3622557765773769$	$604967118391414003$	$101029508536574751093$	$16871927924813680294878$

Jacobians and polarizations

This isogeny class contains the Jacobians of 12 curves (of which all are hyperelliptic), and hence is principally polarizable:

• $y^2=106x^6+119x^5+147x^4+100x^3+14x^2+19x+91$
• $y^2=60x^6+53x^5+100x^4+39x^3+44x^2+35x+105$
• $y^2=150x^6+x^5+86x^3+149x^2+125x+70$
• $y^2=51x^6+132x^5+80x^4+75x^3+58x^2+80x+126$
• $y^2=165x^6+41x^5+20x^4+131x^3+93x^2+157x+48$
• $y^2=73x^6+158x^5+146x^4+138x^3+162x^2+88x+156$
• $y^2=74x^6+163x^5+145x^4+88x^3+41x^2+74$
• $y^2=144x^6+97x^5+157x^4+25x^3+19x^2+157x+148$
• $y^2=146x^6+51x^5+43x^4+7x^3+28x^2+71x+159$
• $y^2=65x^6+59x^5+121x^4+92x^3+153x^2+154x+59$
• $y^2=53x^6+70x^5+75x^4+64x^3+15x^2+150x+160$
• $y^2=76x^6+88x^5+136x^4+82x^3+42x^2+160x+76$

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 4.0.580725.2.

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.bt_bgh	$2$	(not in LMFDB)