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

• Label: 2.163.abs_bey
• 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:	$1 - 44 x + 804 x^{2} - 7172 x^{3} + 26569 x^{4}$
Frobenius angles:	$\pm0.0931167732381$, $\pm0.222413979924$
Angle rank:	$2$ (numerical)
Number field:	4.0.8425728.1
Galois group:	$D_{4}$
Jacobians:	$32$

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$20158$	$697265220$	$18752895499678$	$498332064025030800$	$13239700816595978972398$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$120$	$26242$	$4330176$	$705941014$	$115064180640$	$18755375469874$	$3057125272319112$	$498311414214536926$	$81224760531570974808$	$13239635967067534369282$

Jacobians and polarizations

This isogeny class contains the Jacobians of 32 curves (of which all are hyperelliptic), and hence is principally polarizable:

• $y^2=112x^6+x^5+32x^4+55x^3+76x^2+60x+58$
• $y^2=157x^6+155x^5+159x^4+150x^3+155x^2+124x+110$
• $y^2=122x^6+14x^5+144x^4+146x^3+131x^2+109x+21$
• $y^2=124x^6+132x^5+32x^4+104x^3+33x^2+46x+50$
• $y^2=11x^6+81x^5+155x^4+160x^3+79x^2+99x+32$
• $y^2=142x^6+53x^5+144x^4+85x^3+9x^2+54x+99$
• $y^2=79x^6+69x^5+126x^4+44x^3+33x^2+136x+112$
• $y^2=44x^6+135x^5+96x^4+x^3+147x^2+62x+120$
• $y^2=29x^6+26x^5+67x^4+128x^3+107x^2+84x+121$
• $y^2=116x^6+46x^5+42x^4+124x^3+138x^2+137x+104$
• $y^2=52x^6+114x^5+89x^4+54x^3+60x^2+13x+24$
• $y^2=138x^6+39x^5+32x^4+11x^3+78x^2+153x+64$
• $y^2=77x^6+155x^5+25x^4+63x^3+130x^2+102x+42$
• $y^2=76x^6+7x^5+104x^4+150x^3+115x^2+162x+149$
• $y^2=131x^6+41x^5+x^4+35x^3+92x^2+99x+39$
• $y^2=73x^6+42x^5+94x^4+104x^3+98x^2+133x+123$
• $y^2=83x^6+57x^5+86x^4+84x^3+24x^2+140x+52$
• $y^2=79x^6+3x^5+6x^4+85x^3+44x^2+77x+152$
• $y^2=46x^6+30x^5+53x^4+133x^3+34x^2+139x+26$
• $y^2=136x^6+7x^5+60x^4+159x^3+53x^2+15x+108$
• and

• $y^2=144x^6+51x^5+110x^4+50x^3+116x^2+77x+42$
• $y^2=68x^6+27x^5+112x^4+25x^3+98x^2+50x+85$
• $y^2=43x^6+58x^5+93x^4+145x^3+91x^2+159x+117$
• $y^2=144x^6+43x^5+147x^4+94x^3+77x^2+20x+157$
• $y^2=105x^6+143x^5+4x^4+20x^3+114x^2+112x+26$
• $y^2=40x^6+32x^5+5x^4+10x^3+35x^2+98x+92$
• $y^2=23x^6+129x^5+63x^4+123x^3+76x^2+24x+157$
• $y^2=53x^6+69x^5+12x^4+75x^3+13x^2+153x+127$
• $y^2=134x^6+86x^5+117x^4+88x^3+124x^2+117x+64$
• $y^2=39x^6+101x^5+62x^4+84x^3+25x^2+77x+93$
• $y^2=162x^6+87x^5+119x^4+28x^3+78x^2+71x+70$
• $y^2=46x^6+9x^5+77x^4+89x^3+44x^2+42x+9$

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 4.0.8425728.1.

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.bs_bey	$2$	(not in LMFDB)