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

• Label: 2.163.abt_bfx
• 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:	$1 - 45 x + 829 x^{2} - 7335 x^{3} + 26569 x^{4}$
Frobenius angles:	$\pm0.0992622747912$, $\pm0.199159696144$
Angle rank:	$2$ (numerical)
Number field:	4.0.2319525.8
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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$20019$	$696240801$	$18750113281701$	$498329605649727981$	$13239713117398182381264$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$119$	$26203$	$4329533$	$705937531$	$115064287544$	$18755379226807$	$3057125340863783$	$498311415036903523$	$81224760536549909129$	$13239635967018178444678$

Jacobians and polarizations

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

• $y^2=20x^6+148x^5+20x^4+159x^3+156x^2+156x+94$
• $y^2=89x^6+72x^5+132x^4+98x^3+99x^2+56x+123$
• $y^2=162x^6+147x^5+64x^4+62x^3+2x^2+10x+4$
• $y^2=105x^6+78x^5+96x^4+122x^3+20x^2+125x+19$
• $y^2=106x^6+29x^5+x^4+68x^3+130x^2+11x+84$
• $y^2=20x^6+144x^5+124x^4+74x^3+57x^2+44x+81$
• $y^2=125x^6+103x^5+6x^4+71x^3+96x^2+98x+120$
• $y^2=92x^6+14x^5+131x^4+143x^3+2x^2+30x+80$
• $y^2=30x^6+76x^5+4x^4+5x^3+15x^2+89x+21$
• $y^2=14x^6+34x^5+157x^4+162x^3+112x^2+19x+123$
• $y^2=107x^6+137x^5+6x^4+28x^3+126x^2+38x+23$
• $y^2=114x^6+70x^5+93x^4+94x^3+141x^2+8x+44$
• $y^2=18x^6+70x^5+94x^4+35x^3+94x^2+101x+98$
• $y^2=110x^6+94x^5+66x^4+66x^3+33x^2+115x+120$
• $y^2=108x^6+55x^5+130x^4+155x^3+86x^2+63x+20$
• $y^2=7x^6+97x^5+40x^4+55x^3+158x^2+63x+95$

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 4.0.2319525.8.

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.bt_bfx	$2$	(not in LMFDB)