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

• Label: 2.211.aca_bqb
• 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:	$1 - 52 x + 1093 x^{2} - 10972 x^{3} + 44521 x^{4}$
Frobenius angles:	$\pm0.0756035405235$, $\pm0.195089353530$
Angle rank:	$2$ (numerical)
Number field:	4.0.326225.1
Galois group:	$D_{4}$
Jacobians:	$30$

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$34591$	$1959199649$	$88217618795776$	$3928830940938321209$	$174914329604997819035551$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$160$	$44004$	$9390916$	$1982136324$	$418228008000$	$88245953060358$	$18619893399351040$	$3928797478920648324$	$828976267929789484156$	$174913992535184028475204$

Jacobians and polarizations

This isogeny class contains the Jacobians of 30 curves (of which all are hyperelliptic), and hence is principally polarizable:

• $y^2=72x^6+95x^5+91x^4+138x^3+177x^2+51x+33$
• $y^2=130x^6+175x^5+210x^4+136x^3+104x^2+43x+181$
• $y^2=158x^6+77x^5+102x^4+196x^3+79x^2+50x+130$
• $y^2=179x^6+29x^5+181x^4+48x^3+160x^2+208x+48$
• $y^2=63x^6+203x^5+45x^4+170x^3+101x^2+23x+18$
• $y^2=13x^6+114x^5+198x^4+53x^3+4x^2+194x+112$
• $y^2=43x^6+133x^5+104x^4+98x^3+95x^2+111x+191$
• $y^2=18x^6+9x^5+61x^4+94x^3+9x^2+67x+113$
• $y^2=50x^6+150x^5+56x^4+12x^3+187x^2+24x+15$
• $y^2=97x^6+131x^5+112x^4+198x^3+16x^2+44x+72$
• $y^2=185x^6+134x^5+200x^4+165x^3+118x^2+181x+63$
• $y^2=152x^6+63x^5+122x^4+106x^3+155x^2+169x+160$
• $y^2=171x^6+193x^5+19x^4+90x^3+37x^2+174x+82$
• $y^2=107x^6+194x^5+196x^4+196x^3+120x^2+197x+18$
• $y^2=108x^6+158x^5+180x^4+145x^3+201x^2+72x+17$
• $y^2=89x^6+148x^5+12x^4+9x^3+119x^2+10x+10$
• $y^2=201x^6+110x^5+158x^4+49x^3+168x^2+202x+40$
• $y^2=33x^6+165x^5+22x^4+207x^3+16x^2+157x+98$
• $y^2=166x^6+179x^5+155x^4+10x^3+176x^2+112x+186$
• $y^2=83x^6+99x^5+125x^4+209x^3+91x^2+99$
• $y^2=66x^6+195x^5+136x^4+77x^3+129x^2+130x+104$
• $y^2=132x^6+148x^5+6x^4+154x^3+71x^2+192x+66$
• $y^2=94x^6+99x^5+13x^4+9x^2+149x+126$
• $y^2=153x^6+110x^5+167x^4+65x^3+146x^2+119x+138$
• $y^2=155x^6+181x^5+200x^4+92x^3+127x^2+26x+59$
• $y^2=93x^6+128x^5+200x^4+133x^3+94x^2+199x+146$
• $y^2=68x^6+19x^5+98x^4+80x^3+166x^2+172x+155$
• $y^2=92x^6+118x^5+57x^4+196x^3+44x^2+66x+48$
• $y^2=5x^6+30x^5+177x^4+208x^3+146x^2+66x+186$
• $y^2=126x^6+x^5+57x^4+114x^3+69x^2+29x+117$

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 4.0.326225.1.

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_bqb	$2$	(not in LMFDB)