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

• Label: 2.163.abr_bdz
• 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:	$1 - 43 x + 779 x^{2} - 7009 x^{3} + 26569 x^{4}$
Frobenius angles:	$\pm0.0890585227448$, $\pm0.242810877127$
Angle rank:	$2$ (numerical)
Number field:	4.0.21188013.2
Galois group:	$D_{4}$
Jacobians:	$16$

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$20297$	$698237097$	$18755184408299$	$498332400553350189$	$13239683683148189537072$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$121$	$26279$	$4330705$	$705941491$	$115064031736$	$18755371681067$	$3057125218114879$	$498311413803220819$	$81224760533430763291$	$13239635967183291134534$

Jacobians and polarizations

This isogeny class contains the Jacobians of 16 curves (of which all are hyperelliptic), and hence is principally polarizable:

• $y^2=10x^6+153x^5+155x^4+77x^3+90x^2+146x+20$
• $y^2=122x^6+24x^5+61x^4+148x^3+4x^2+96x+64$
• $y^2=34x^6+5x^5+147x^4+31x^3+13x^2+3x+89$
• $y^2=70x^6+5x^5+30x^4+58x^3+28x^2+85x+147$
• $y^2=55x^6+38x^5+56x^4+46x^3+89x^2+62x+86$
• $y^2=138x^6+131x^5+157x^4+69x^3+37x^2+42x+105$
• $y^2=26x^6+4x^5+114x^4+130x^3+59x^2+77x+1$
• $y^2=31x^6+150x^5+128x^4+110x^3+133x^2+103x+100$
• $y^2=136x^6+36x^5+24x^4+87x^3+162x^2+11x+76$
• $y^2=81x^6+2x^5+29x^4+14x^3+107x^2+30x+82$
• $y^2=162x^6+34x^5+67x^4+33x^3+51x^2+111x+98$
• $y^2=62x^6+158x^5+119x^4+98x^3+145x^2+80x+134$
• $y^2=63x^6+43x^5+150x^4+49x^3+80x^2+13x+17$
• $y^2=16x^6+36x^5+151x^4+19x^3+108x^2+68x+6$
• $y^2=6x^6+117x^5+61x^4+11x^3+110x^2+145x+138$
• $y^2=12x^6+130x^5+81x^4+50x^3+46x^2+157x+86$

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 4.0.21188013.2.

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_bdz	$2$	(not in LMFDB)