Abelian variety isogeny class 2.211.abz_bow over $\F_{211}$

• Label: 2.211.abz_bow
• Base field: $\F_{211}$
• 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:	$\F_{211}$
Dimension:	$2$
L-polynomial:	$1 - 51 x + 1062 x^{2} - 10761 x^{3} + 44521 x^{4}$
Frobenius angles:	$\pm0.0494678005613$, $\pm0.221478659304$
Angle rank:	$2$ (numerical)
Number field:	4.0.2946793.1
Galois group:	$D_{4}$
Jacobians:	$28$

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$34772$	$1961001712$	$88222945496528$	$3928819277650398400$	$174914117291875049955452$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$161$	$44045$	$9391484$	$1982130441$	$418227500351$	$88245938058662$	$18619893092787581$	$3928797474126181201$	$828976267872888118724$	$174913992534740849191805$

Jacobians and polarizations

This isogeny class contains the Jacobians of 28 curves (of which all are hyperelliptic), and hence is principally polarizable:

• $y^2=100x^6+52x^5+7x^4+147x^3+74x^2+12x+98$
• $y^2=75x^6+185x^5+30x^4+21x^3+72x^2+187x+67$
• $y^2=165x^6+59x^5+182x^4+166x^3+76x^2+158x+67$
• $y^2=114x^6+191x^5+177x^4+36x^3+38x^2+186x+114$
• $y^2=90x^6+6x^5+115x^4+194x^3+51x^2+6x+48$
• $y^2=130x^6+63x^5+163x^4+194x^3+102x^2+115x+191$
• $y^2=36x^6+119x^5+66x^4+109x^3+181x^2+70x+56$
• $y^2=175x^6+2x^5+12x^4+130x^3+105x^2+45x+88$
• $y^2=73x^6+180x^5+180x^4+149x^3+208x^2+57x+86$
• $y^2=198x^6+150x^5+124x^4+177x^3+85x^2+168x+103$
• $y^2=104x^6+16x^5+111x^4+197x^3+99x^2+150x+46$
• $y^2=208x^6+165x^5+3x^4+128x^3+x^2+191x+79$
• $y^2=108x^6+59x^5+165x^4+154x^3+147x^2+87x+159$
• $y^2=202x^6+72x^5+95x^4+144x^3+125x^2+52x+8$
• $y^2=171x^6+90x^5+203x^4+172x^3+6x^2+50x+107$
• $y^2=39x^6+8x^5+26x^4+118x^3+38x^2+173x+196$
• $y^2=110x^6+92x^5+18x^4+144x^3+26x^2+112x+116$
• $y^2=22x^6+192x^5+40x^4+25x^3+28x^2+62x+26$
• $y^2=144x^6+160x^5+78x^4+60x^3+207x^2+156x+106$
• $y^2=184x^6+99x^5+157x^4+208x^3+159x^2+133x+192$
• $y^2=48x^6+55x^5+115x^4+18x^3+5x^2+141x+208$
• $y^2=168x^6+175x^5+24x^4+43x^3+143x^2+95x$
• $y^2=166x^6+54x^5+141x^4+63x^3+15x^2+51x+86$
• $y^2=118x^6+158x^5+5x^4+136x^3+199x^2+10x+160$
• $y^2=23x^6+25x^5+197x^4+93x^3+68x^2+189x+98$
• $y^2=174x^6+177x^5+101x^4+12x^3+24x^2+171x+185$
• $y^2=4x^6+197x^5+171x^4+200x^3+117x^2+22x+193$
• $y^2=2x^6+34x^5+165x^3+61x^2+166x+49$

Decomposition and endomorphism algebra

All geometric endomorphisms are defined over $\F_{211}$.

Endomorphism algebra over $\F_{211}$

The endomorphism algebra of this simple isogeny class is 4.0.2946793.1.

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
2.211.bz_bow	$2$	(not in LMFDB)