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

• Label: 2.211.acb_brf
• 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:	$1 - 53 x + 1123 x^{2} - 11183 x^{3} + 44521 x^{4}$
Frobenius angles:	$\pm0.100415912064$, $\pm0.161724857299$
Angle rank:	$2$ (numerical)
Number field:	4.0.405725.1
Galois group:	$D_{4}$
Jacobians:	$9$

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$34409$	$1957218329$	$88209614320475$	$3928822410397201229$	$174914442152243466157584$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$159$	$43959$	$9390063$	$1982132019$	$418228277104$	$88245964284843$	$18619893674689809$	$3928797484013624979$	$828976268003313010413$	$174913992535943176092454$

Jacobians and polarizations

This isogeny class contains the Jacobians of 9 curves (of which all are hyperelliptic), and hence is principally polarizable:

• $y^2=163x^6+92x^5+208x^4+207x^3+95x^2+142x+54$
• $y^2=205x^6+115x^5+24x^4+208x^3+163x^2+48x+206$
• $y^2=102x^6+196x^5+126x^4+150x^3+160x^2+192x+101$
• $y^2=108x^6+122x^5+31x^4+54x^3+186x^2+173x+145$
• $y^2=x^6+82x^5+154x^4+2x^3+124x^2+49x+140$
• $y^2=132x^6+103x^5+159x^4+134x^3+29x^2+145x+5$
• $y^2=95x^6+113x^5+110x^4+7x^3+209x^2+154x+198$
• $y^2=64x^6+138x^5+166x^4+170x^3+155x^2+93x+146$
• $y^2=203x^6+133x^5+41x^3+72x^2+35x+23$

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 4.0.405725.1.

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.cb_brf	$2$	(not in LMFDB)