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

• Label: 2.163.abr_bdt
• Base field: $\F_{163}$
• 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:	$\F_{163}$
Dimension:	$2$
L-polynomial:	$1 - 43 x + 773 x^{2} - 7009 x^{3} + 26569 x^{4}$
Frobenius angles:	$\pm0.0320302473605$, $\pm0.258019905074$
Angle rank:	$2$ (numerical)
Number field:	4.0.8383413.1
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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$20291$	$697908945$	$18751827473333$	$498314220556214925$	$13239615404212376661296$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$121$	$26267$	$4329931$	$705915739$	$115063438336$	$18755361143399$	$3057125066250145$	$498311411956337251$	$81224760513175135303$	$13239635966952406107782$

Jacobians and polarizations

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

• $y^2=149 x^6+95 x^5+21 x^4+122 x^3+130 x^2+18 x+92$
• $y^2=125 x^6+92 x^5+79 x^4+104 x^3+6 x^2+123 x+20$
• $y^2=88 x^6+71 x^5+132 x^4+85 x^3+133 x^2+152 x+87$
• $y^2=143 x^6+23 x^5+43 x^4+12 x^3+132 x^2+134 x+94$
• $y^2=151 x^6+111 x^5+81 x^4+108 x^3+92 x^2+145 x+122$
• $y^2=109 x^6+139 x^5+152 x^4+130 x^3+104 x^2+150 x+78$
• $y^2=29 x^6+135 x^5+41 x^4+53 x^3+89 x^2+95 x+89$
• $y^2=123 x^6+54 x^5+25 x^4+10 x^3+142 x^2+110 x+56$
• $y^2=11 x^6+140 x^5+15 x^4+40 x^3+112 x^2+39 x+53$
• $y^2=115 x^6+155 x^5+20 x^4+152 x^3+32 x^2+72 x+129$
• $y^2=112 x^6+59 x^5+143 x^4+54 x^3+159 x^2+104 x+79$
• $y^2=88 x^6+113 x^5+28 x^4+43 x^3+147 x^2+74 x+116$

Decomposition and endomorphism algebra

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

Endomorphism algebra over $\F_{163}$

The endomorphism algebra of this simple isogeny class is 4.0.8383413.1.

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
2.163.br_bdt	$2$	(not in LMFDB)