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

• Label: 2.211.aca_bpy
• 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:	$1 - 52 x + 1090 x^{2} - 10972 x^{3} + 44521 x^{4}$
Frobenius angles:	$\pm0.0394870506560$, $\pm0.206103458070$
Angle rank:	$2$ (numerical)
Number field:	4.0.63488.1
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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$34588$	$1958925968$	$88213217248828$	$3928792584545503232$	$174914090813263149684508$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$160$	$43998$	$9390448$	$1982116974$	$418227437040$	$88245939644814$	$18619893135034624$	$3928797474436328670$	$828976267863344632384$	$174913992534315589811518$

Jacobians and polarizations

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

• $y^2=195x^6+70x^5+133x^4+114x^3+157x^2+188x+25$
• $y^2=32x^6+51x^5+137x^4+192x^3+21x^2+109x+50$
• $y^2=168x^6+56x^5+59x^4+135x^3+91x^2+172x+195$
• $y^2=98x^6+180x^5+134x^4+98x^3+164x^2+61x+21$
• $y^2=86x^6+59x^5+55x^4+177x^3+209x^2+50x+29$
• $y^2=12x^6+165x^5+56x^4+71x^3+164x^2+116x+63$
• $y^2=123x^6+48x^5+56x^4+176x^3+102x^2+125x+36$
• $y^2=93x^6+144x^5+80x^4+194x^3+72x^2+194x+188$
• $y^2=172x^6+120x^5+152x^4+100x^3+20x^2+54x+30$
• $y^2=68x^6+178x^5+155x^4+11x^3+105x^2+160x+7$
• $y^2=94x^6+90x^5+35x^4+105x^3+156x^2+26x+187$
• $y^2=112x^6+184x^5+78x^4+147x^3+22x^2+73x+178$
• $y^2=126x^6+79x^5+19x^4+131x^3+170x^2+44x+81$
• $y^2=183x^6+75x^5+8x^4+138x^3+154x^2+126x+189$
• $y^2=90x^6+95x^5+72x^4+128x^3+186x^2+22x+26$
• $y^2=28x^6+52x^5+189x^4+195x^3+49x^2+13x+185$
• $y^2=54x^6+164x^5+160x^4+46x^3+23x^2+141x+159$
• $y^2=70x^6+198x^5+130x^4+121x^3+158x^2+149x+44$
• $y^2=118x^6+76x^5+49x^4+163x^3+53x^2+165x+167$
• $y^2=173x^6+86x^5+199x^4+166x^3+10x^2+198x+70$
• $y^2=150x^6+77x^5+149x^4+31x^3+176x^2+25x+186$
• $y^2=9x^6+139x^5+109x^4+188x^3+80x^2+198x+7$
• $y^2=123x^6+132x^5+167x^4+72x^3+30x^2+130x+53$
• $y^2=100x^6+173x^5+206x^4+8x^3+11x^2+180x+186$
• $y^2=166x^6+133x^5+181x^4+35x^3+18x^2+202x+86$
• $y^2=5x^6+183x^5+11x^4+73x^3+140x^2+52x+8$
• $y^2=78x^6+204x^5+210x^4+34x^3+58x^2+60x+187$
• $y^2=178x^6+115x^5+135x^4+17x^3+109x^2+127x+85$

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 4.0.63488.1.

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.ca_bpy	$2$	(not in LMFDB)