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

• Label: 2.173.abw_bjj
• 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:	$1 - 48 x + 919 x^{2} - 8304 x^{3} + 29929 x^{4}$
Frobenius angles:	$\pm0.0666081623220$, $\pm0.178705272832$
Angle rank:	$2$ (numerical)
Number field:	4.0.843408.1
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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$22497$	$881904897$	$26792358779124$	$802356772797220329$	$24013861995771846125097$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$126$	$29464$	$5174550$	$895742356$	$154964241486$	$26808760211182$	$4637914408067094$	$802359179053500004$	$138808137875741662446$	$24013807852522296546184$

Jacobians and polarizations

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

• $y^2=123x^6+155x^5+35x^4+81x^3+26x^2+38x+48$
• $y^2=153x^6+9x^5+51x^4+42x^3+155x^2+138x+153$
• $y^2=147x^6+86x^5+168x^4+65x^3+145x^2+14x+120$
• $y^2=43x^6+148x^5+59x^4+87x^3+135x^2+58x+153$
• $y^2=65x^6+83x^5+84x^4+74x^3+104x^2+28x+161$
• $y^2=160x^6+24x^5+142x^4+162x^3+14x^2+123x+2$
• $y^2=94x^6+126x^5+125x^4+63x^3+131x^2+36x+67$
• $y^2=39x^6+69x^5+118x^4+78x^3+172x^2+150x+125$
• $y^2=11x^6+132x^5+11x^4+58x^3+137x^2+99x+131$
• $y^2=84x^6+86x^5+101x^4+25x^3+169x^2+36x+142$

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 4.0.843408.1.

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.bw_bjj	$2$	(not in LMFDB)