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

• Label: 2.173.abv_bij
• 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:	$1 - 47 x + 893 x^{2} - 8131 x^{3} + 29929 x^{4}$
Frobenius angles:	$\pm0.0630646735849$, $\pm0.201502091012$
Angle rank:	$2$ (numerical)
Number field:	4.0.2863413.1
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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$22645$	$883177645$	$26796833870065$	$802365499477709125$	$24013862943484532473600$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$127$	$29507$	$5175415$	$895752099$	$154964247602$	$26808757673339$	$4637914339328411$	$802359177884002531$	$138808137861695194795$	$24013807852425029980982$

Jacobians and polarizations

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

• $y^2=72x^6+107x^5+104x^4+25x^3+20x^2+6x+87$
• $y^2=7x^6+64x^5+75x^4+158x^3+61x^2+87x+127$
• $y^2=86x^6+15x^5+38x^4+142x^3+144x^2+47x+109$
• $y^2=50x^6+44x^5+65x^4+37x^3+64x^2+15x+78$
• $y^2=42x^6+31x^5+147x^4+63x^3+151x^2+31x+134$
• $y^2=43x^6+46x^5+158x^4+24x^3+101x^2+80x+25$
• $y^2=32x^6+18x^5+14x^4+84x^3+162x^2+30x+39$
• $y^2=4x^6+65x^5+133x^4+84x^3+96x^2+158x+128$
• $y^2=19x^6+88x^5+13x^4+150x^3+61x^2+77x+3$
• $y^2=61x^6+169x^5+43x^4+116x^3+129x^2+46x+114$
• $y^2=59x^6+141x^5+16x^4+107x^3+19x^2+45x+64$
• $y^2=20x^6+61x^5+86x^4+151x^3+107x^2+51x+103$

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 4.0.2863413.1.

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.bv_bij	$2$	(not in LMFDB)