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

• Label: 2.211.aby_bnx
• 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:	$1 - 50 x + 1037 x^{2} - 10550 x^{3} + 44521 x^{4}$
Frobenius angles:	$\pm0.0789664157985$, $\pm0.229241198235$
Angle rank:	$2$ (numerical)
Number field:	4.0.29889600.1
Galois group:	$D_{4}$
Jacobians:	$24$

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$34959$	$1963262481$	$88235609722884$	$3928871502398853225$	$174914301919330682303079$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$162$	$44096$	$9392832$	$1982156788$	$418227941802$	$88245945253406$	$18619893219397422$	$3928797476547468388$	$828976267919261763792$	$174913992535560720003056$

Jacobians and polarizations

This isogeny class contains the Jacobians of 24 curves (of which all are hyperelliptic), and hence is principally polarizable:

• $y^2=49x^6+107x^5+192x^4+174x^3+179x^2+37x+10$
• $y^2=74x^6+196x^5+134x^4+110x^3+187x^2+105x+127$
• $y^2=96x^6+57x^5+150x^4+170x^3+64x^2+151x+86$
• $y^2=172x^6+44x^5+200x^4+108x^3+87x^2+76x+39$
• $y^2=19x^6+125x^5+144x^4+151x^3+75x^2+15x+172$
• $y^2=200x^6+99x^5+46x^4+27x^3+135x^2+196x+174$
• $y^2=44x^6+90x^5+61x^4+122x^3+10x^2+164x+157$
• $y^2=64x^6+86x^5+32x^4+145x^3+191x^2+111x+6$
• $y^2=74x^6+20x^5+113x^4+87x^3+101x^2+64x+151$
• $y^2=157x^6+53x^5+62x^4+36x^3+187x^2+73x+114$
• $y^2=161x^6+181x^5+43x^4+184x^3+66x^2+119x+155$
• $y^2=44x^6+121x^5+198x^4+137x^3+130x^2+169x+48$
• $y^2=40x^6+99x^5+10x^4+149x^3+61x^2+208x+27$
• $y^2=157x^6+161x^4+56x^3+182x^2+202x+98$
• $y^2=164x^6+155x^5+x^4+160x^3+74x^2+59x+207$
• $y^2=24x^6+128x^5+176x^4+170x^3+150x^2+108x+160$
• $y^2=161x^6+207x^5+46x^4+125x^3+181x^2+209x+110$
• $y^2=12x^6+127x^5+124x^4+22x^3+203x^2+113x+31$
• $y^2=13x^6+82x^5+47x^4+39x^3+204x^2+42x+107$
• $y^2=178x^6+165x^5+91x^4+194x^3+113x^2+74x+78$
• $y^2=29x^6+69x^5+35x^4+131x^3+132x^2+198x+85$
• $y^2=152x^6+97x^5+147x^4+96x^3+157x^2+110x+186$
• $y^2=209x^6+59x^5+114x^4+136x^3+158x^2+64x+98$
• $y^2=100x^6+122x^5+46x^4+114x^3+197x^2+157x+140$

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 4.0.29889600.1.

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.by_bnx	$2$	(not in LMFDB)