Abelian variety isogeny class 2.173.abt_bgg over $\F_{173}$

• Label: 2.173.abt_bgg
• Base field: $\F_{173}$
• 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:	$\F_{173}$
Dimension:	$2$
L-polynomial:	$1 - 45 x + 838 x^{2} - 7785 x^{3} + 29929 x^{4}$
Frobenius angles:	$\pm0.0154486843224$, $\pm0.247870790543$
Angle rank:	$2$ (numerical)
Number field:	4.0.1806444.1
Galois group:	$D_{4}$
Jacobians:	$10$

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$22938$	$885360924$	$26801759572056$	$802360164759947136$	$24013778529438943026018$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$129$	$29581$	$5176368$	$895746145$	$154963702869$	$26808743828122$	$4637914106334393$	$802359175029023329$	$138808137837378759264$	$24013807852316095005061$

Jacobians and polarizations

This isogeny class contains the Jacobians of 10 curves (of which all are hyperelliptic), and hence is principally polarizable:

• $y^2=22x^6+170x^5+134x^4+97x^3+41x^2+127x+87$
• $y^2=100x^6+154x^5+5x^4+116x^3+126x^2+92x+131$
• $y^2=12x^6+44x^5+171x^4+43x^3+167x+151$
• $y^2=32x^6+92x^5+85x^4+38x^3+32x^2+109x+59$
• $y^2=135x^6+151x^5+42x^4+27x^3+87x^2+53x+74$
• $y^2=130x^6+70x^5+169x^4+131x^3+72x^2+123x+131$
• $y^2=42x^6+132x^5+126x^4+24x^3+83x^2+103x+109$
• $y^2=115x^6+5x^5+71x^4+56x^3+115x^2+66x+17$
• $y^2=78x^6+87x^5+115x^4+24x^3+62x^2+31x+2$
• $y^2=126x^6+62x^5+33x^4+155x^3+7x^2+159x+5$

Decomposition and endomorphism algebra

All geometric endomorphisms are defined over $\F_{173}$.

Endomorphism algebra over $\F_{173}$

The endomorphism algebra of this simple isogeny class is 4.0.1806444.1.

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
2.173.bt_bgg	$2$	(not in LMFDB)