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

• Label: 2.211.aby_bnu
• 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:	$1 - 50 x + 1034 x^{2} - 10550 x^{3} + 44521 x^{4}$
Frobenius angles:	$\pm0.0558555089574$, $\pm0.236511340633$
Angle rank:	$2$ (numerical)
Number field:	4.0.186576.2
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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$34956$	$1962989136$	$88231377951324$	$3928836666852451584$	$174914101169861978282076$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$162$	$44090$	$9392382$	$1982139214$	$418227461802$	$88245935056586$	$18619893042724422$	$3928797473992604254$	$828976267887862722642$	$174913992535217041881050$

Jacobians and polarizations

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

• $y^2=93x^6+42x^5+62x^4+59x^3+130x^2+167x+19$
• $y^2=191x^6+198x^5+39x^4+85x^3+92x^2+26x+137$
• $y^2=129x^5+133x^4+8x^3+149x^2+159x+155$
• $y^2=88x^6+209x^5+114x^4+8x^3+142x^2+104x+159$
• $y^2=122x^6+80x^5+55x^4+137x^3+207x^2+58x+146$
• $y^2=143x^6+62x^5+193x^4+125x^3+17x^2+70x+135$
• $y^2=114x^6+186x^5+36x^4+85x^3+188x^2+124x+57$
• $y^2=47x^6+100x^5+86x^4+63x^3+4x^2+166x+185$
• $y^2=189x^6+61x^5+4x^4+89x^3+20x^2+53x+35$
• $y^2=185x^6+23x^5+53x^4+198x^3+138x^2+22x+140$
• $y^2=195x^6+88x^5+20x^4+10x^3+30x^2+89x+130$
• $y^2=52x^6+34x^5+164x^4+8x^3+129x^2+147x+127$
• $y^2=2x^6+120x^5+108x^4+9x^3+153x^2+28x+59$
• $y^2=204x^6+30x^5+204x^4+114x^3+152x^2+168x+177$
• $y^2=152x^6+188x^5+27x^4+65x^3+117x^2+190x+113$
• $y^2=99x^6+205x^5+150x^4+185x^3+135x^2+117x+112$
• $y^2=30x^6+162x^5+116x^4+34x^3+53x^2+138x+108$
• $y^2=89x^5+151x^4+54x^3+14x^2+201x+191$
• $y^2=105x^6+115x^5+5x^4+114x^3+157x^2+189x+50$
• $y^2=62x^6+129x^5+66x^4+18x^3+202x^2+34x+145$
• and

• $y^2=114x^6+64x^5+142x^4+194x^3+150x^2+77x+188$
• $y^2=158x^6+142x^5+36x^4+26x^3+120x^2+206x+187$
• $y^2=12x^6+184x^5+158x^4+192x^3+104x^2+85x+95$
• $y^2=180x^6+71x^5+173x^4+55x^3+50x^2+162x+149$
• $y^2=27x^6+165x^5+101x^4+2x^3+163x^2+103x+11$
• $y^2=161x^6+126x^5+200x^4+43x^3+74x^2+166x+205$
• $y^2=59x^6+38x^5+203x^4+182x^3+180x^2+59x+160$
• $y^2=71x^6+145x^5+62x^4+129x^3+137x^2+x+157$
• $y^2=29x^6+99x^5+91x^4+138x^3+104x^2+53x+106$
• $y^2=183x^6+111x^5+58x^4+46x^3+120x^2+97x+154$
• $y^2=90x^6+14x^5+46x^4+122x^3+x^2+112x+186$
• $y^2=3x^6+42x^5+30x^4+42x^3+93x^2+155x+188$
• $y^2=133x^6+138x^5+150x^4+4x^3+90x^2+9x+68$
• $y^2=164x^6+79x^5+187x^4+35x^3+188x^2+78x+137$
• $y^2=102x^6+25x^5+21x^4+27x^3+187x^2+136x+154$
• $y^2=99x^6+172x^5+129x^4+153x^3+136x^2+191x+74$
• $y^2=18x^6+49x^5+157x^4+36x^3+191x^2+138x+210$
• $y^2=130x^6+117x^5+65x^4+23x^2+157x+35$
• $y^2=137x^6+107x^5+86x^4+23x^3+39x^2+83x+126$
• $y^2=142x^6+120x^5+162x^4+30x^3+59x^2+172x+74$
• $y^2=207x^6+10x^5+76x^4+35x^3+48x^2+161x+77$
• $y^2=104x^6+84x^5+165x^4+108x^3+120x^2+160x+110$
• $y^2=4x^6+20x^5+29x^4+127x^3+72x^2+43x+101$
• $y^2=122x^6+21x^5+77x^4+185x^3+86x^2+114x+121$
• $y^2=42x^6+89x^5+9x^4+43x^3+22x^2+5x+40$
• $y^2=183x^6+148x^5+158x^4+177x^3+4x^2+91x+28$
• $y^2=70x^6+202x^5+46x^4+197x^3+130x^2+46x+66$
• $y^2=126x^6+115x^5+155x^4+79x^3+81x^2+174x+203$

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 4.0.186576.2.

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
2.211.by_bnu	$2$	(not in LMFDB)