Abelian variety isogeny class 2.163.abw_bis over $\F_{163}$

• Label: 2.163.abw_bis
• Base field: $\F_{163}$
• Dimension: $2$
• $p$-rank: $2$
• Ordinary: yes
• Supersingular: no
• Simple: no
• Geometrically simple: no
• Primitive: yes
• Principally polarizable: yes
• Contains a Jacobian: yes

Invariants

Base field:	$\F_{163}$
Dimension:	$2$
L-polynomial:	$( 1 - 24 x + 163 x^{2} )^{2}$
	$1 - 48 x + 902 x^{2} - 7824 x^{3} + 26569 x^{4}$
Frobenius angles:	$\pm0.110906256499$, $\pm0.110906256499$
Angle rank:	$1$ (numerical)
Jacobians:	$14$

This isogeny class is not 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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$19600$	$692742400$	$18737297395600$	$498298198325760000$	$13239662582857049290000$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$116$	$26070$	$4326572$	$705893038$	$115063848356$	$18755378181510$	$3057125409995612$	$498311416966474078$	$81224760569903050196$	$13239635967451661911350$

Jacobians and polarizations

This isogeny class contains the Jacobians of 14 curves (of which all are hyperelliptic), and hence is principally polarizable:

• $y^2=16x^6+99x^4+99x^2+16$
• $y^2=6x^6+140x^5+121x^4+124x^3+121x^2+140x+6$
• $y^2=58x^6+101x^5+36x^4+91x^3+74x^2+129x+20$
• $y^2=52x^6+150x^5+51x^4+51x^3+54x^2+83x+32$
• $y^2=112x^6+89x^5+42x^4+161x^3+128x^2+121x+162$
• $y^2=118x^6+70x^4+70x^2+118$
• $y^2=52x^6+102x^5+37x^4+145x^3+79x^2+145x+20$
• $y^2=34x^6+23x^5+139x^4+104x^3+139x^2+23x+34$
• $y^2=52x^6+26x^5+95x^4+81x^3+95x^2+26x+52$
• $y^2=118x^6+97x^5+20x^4+x^3+129x^2+132x+10$
• $y^2=113x^6+103x^4+103x^2+113$
• $y^2=109x^6+70x^5+123x^4+73x^3+117x^2+7x+103$
• $y^2=107x^6+16x^5+115x^4+130x^3+115x^2+16x+107$
• $y^2=121x^6+6x^5+128x^4+124x^3+19x^2+71x+99$

Decomposition and endomorphism algebra

All geometric endomorphisms are defined over $\F_{163}$.

Endomorphism algebra over $\F_{163}$

The isogeny class factors as 1.163.ay^2 and its endomorphism algebra is $\mathrm{M}_{2}($\(\Q(\sqrt{-19}) \)$)$

Base change

This is a primitive isogeny class.

Twists

Below are some of the twists of this isogeny class.

Twist	Extension degree	Common base change
2.163.a_ajq	$2$	(not in LMFDB)
2.163.bw_bis	$2$	(not in LMFDB)
2.163.y_px	$3$	(not in LMFDB)