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

• Label: 2.163.abr_bdy
• 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:	$1 - 43 x + 778 x^{2} - 7009 x^{3} + 26569 x^{4}$
Frobenius angles:	$\pm0.0815159038334$, $\pm0.245687237918$
Angle rank:	$2$ (numerical)
Number field:	4.0.5575877.1
Galois group:	$D_{4}$
Jacobians:	$48$

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$20296$	$698182400$	$18754624907488$	$498329377601408000$	$13239672427012164614296$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$121$	$26277$	$4330576$	$705937209$	$115063933911$	$18755369984694$	$3057125195108245$	$498311413563929841$	$81224760531726545968$	$13239635967179480706757$

Jacobians and polarizations

This isogeny class contains the Jacobians of 48 curves (of which all are hyperelliptic), and hence is principally polarizable:

• $y^2=90x^6+143x^5+147x^4+158x^3+30x^2+149x+82$
• $y^2=41x^6+39x^5+123x^4+27x^3+34x^2+13x+86$
• $y^2=23x^6+84x^5+124x^4+101x^3+81x^2+91x+74$
• $y^2=35x^6+41x^5+45x^4+93x^3+25x^2+61x+19$
• $y^2=78x^6+58x^5+63x^4+34x^3+105x^2+47x+20$
• $y^2=63x^6+139x^5+118x^4+150x^3+28x^2+46x+94$
• $y^2=80x^6+6x^5+78x^4+40x^3+24x^2+29x+31$
• $y^2=52x^6+33x^5+9x^4+53x^3+77x^2+5x+127$
• $y^2=58x^6+25x^5+35x^4+24x^3+124x^2+106x+54$
• $y^2=95x^6+78x^5+102x^4+37x^3+114x^2+92x+72$
• $y^2=39x^6+157x^5+17x^4+97x^3+34x^2+119x+27$
• $y^2=141x^6+95x^5+154x^4+70x^3+41x^2+10x+17$
• $y^2=18x^6+148x^5+3x^4+39x^3+9x^2+142x+104$
• $y^2=29x^6+39x^5+55x^4+121x^3+33x^2+73x+20$
• $y^2=158x^6+126x^5+110x^4+61x^3+53x^2+87x+123$
• $y^2=159x^6+61x^5+84x^4+116x^3+44x^2+8x+11$
• $y^2=143x^6+139x^4+160x^3+17x^2+123x+11$
• $y^2=156x^6+160x^5+138x^4+10x^3+21x^2+80x+51$
• $y^2=32x^6+115x^5+25x^4+95x^3+110x^2+156x+144$
• $y^2=56x^6+5x^5+144x^4+42x^3+100x^2+158x+8$
• and

• $y^2=13x^6+16x^5+127x^4+143x^3+125x^2+100x+88$
• $y^2=97x^6+73x^5+122x^4+103x^3+92x^2+42x+42$
• $y^2=162x^6+97x^5+157x^4+49x^3+122x^2+95x+29$
• $y^2=79x^6+122x^5+145x^4+132x^3+134x^2+63x+8$
• $y^2=44x^6+106x^5+43x^4+133x^3+125x^2+76x+157$
• $y^2=63x^6+72x^5+161x^4+49x^3+23x^2+139x+124$
• $y^2=91x^6+38x^5+141x^4+44x^3+94x^2+59x+106$
• $y^2=159x^6+146x^5+15x^4+10x^3+72x^2+118x+37$
• $y^2=56x^6+143x^5+38x^4+58x^3+154x^2+74x+143$
• $y^2=160x^6+5x^5+99x^3+43x^2+76x+142$
• $y^2=158x^6+81x^5+107x^4+26x^3+143x^2+96x+26$
• $y^2=54x^6+45x^5+91x^4+154x^3+146x^2+50x+8$
• $y^2=9x^6+90x^5+78x^4+161x^3+38x^2+8x+29$
• $y^2=20x^6+99x^5+162x^4+51x^3+107x^2+94x+147$
• $y^2=102x^6+134x^5+156x^4+15x^3+102x^2+123x+137$
• $y^2=71x^6+141x^5+120x^4+7x^3+56x^2+154$
• $y^2=155x^6+72x^5+6x^4+103x^2+70x+26$
• $y^2=135x^6+16x^5+76x^4+84x^3+136x^2+77x+32$
• $y^2=112x^6+99x^5+17x^4+52x^3+133x^2+29x+45$
• $y^2=2x^6+15x^5+162x^4+103x^3+152x^2+12x+59$
• $y^2=151x^6+59x^5+72x^4+150x^3+141x^2+105x+5$
• $y^2=76x^6+162x^5+25x^4+139x^3+136x^2+124x+152$
• $y^2=160x^6+123x^5+47x^4+157x^3+117x^2+83x+95$
• $y^2=26x^6+22x^5+155x^4+32x^3+28x^2+102x+14$
• $y^2=42x^6+45x^5+94x^4+54x^3+135x^2+119x+80$
• $y^2=78x^6+63x^5+101x^4+99x^3+65x^2+37x+61$
• $y^2=64x^6+162x^5+36x^4+113x^3+110x^2+94x+27$
• $y^2=8x^6+114x^5+81x^4+47x^3+60x^2+17x+99$

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 4.0.5575877.1.

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_bdy	$2$	(not in LMFDB)