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

• Label: 2.211.abz_bou
• Base field: $\F_{211}$
• Dimension: $2$
• $p$-rank: $2$
• Ordinary: yes
• Supersingular: no
• Simple: no
• Geometrically simple: no
• Primitive: yes
• Principally polarizable: yes
• Contains a Jacobian: yes

Invariants

Base field:	$\F_{211}$
Dimension:	$2$
L-polynomial:	$( 1 - 29 x + 211 x^{2} )( 1 - 22 x + 211 x^{2} )$
	$1 - 51 x + 1060 x^{2} - 10761 x^{3} + 44521 x^{4}$
Frobenius angles:	$\pm0.0189887838440$, $\pm0.226532097096$
Angle rank:	$2$ (numerical)
Jacobians:	$10$

This isogeny class is not 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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$34770$	$1960819380$	$88220067759000$	$3928794856603362720$	$174913970117386007466750$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$161$	$44041$	$9391178$	$1982118121$	$418227148451$	$88245930078178$	$18619892940441401$	$3928797471574393681$	$828976267833683407598$	$174913992534153677638201$

Jacobians and polarizations

This isogeny class contains the Jacobians of 10 curves (of which all are hyperelliptic), and hence is principally polarizable:

• $y^2=155x^6+45x^5+5x^4+24x^3+74x^2+207x+42$
• $y^2=5x^6+187x^5+72x^4+110x^3+95x^2+172x+166$
• $y^2=146x^6+16x^5+52x^4+177x^3+140x^2+107x+35$
• $y^2=2x^6+113x^5+86x^4+124x^3+17x^2+27x+131$
• $y^2=34x^6+151x^5+27x^4+92x^3+206x^2+15x+132$
• $y^2=146x^6+127x^5+16x^4+22x^3+144x^2+99x+116$
• $y^2=64x^6+60x^5+143x^4+136x^3+188x^2+170x+97$
• $y^2=76x^6+8x^5+23x^4+92x^3+191x^2+147x+185$
• $y^2=106x^6+33x^5+84x^4+24x^3+23x^2+109x+29$
• $y^2=125x^6+90x^5+183x^4+103x^3+202x^2+197x+141$

Decomposition and endomorphism algebra

All geometric endomorphisms are defined over $\F_{211}$.

Endomorphism algebra over $\F_{211}$

The isogeny class factors as 1.211.abd $\times$ 1.211.aw and its endomorphism algebra is a direct product of the endomorphism algebras for each isotypic factor. The endomorphism algebra for each factor is:

• 1.211.abd : \(\Q(\sqrt{-3}) \).
• 1.211.aw : \(\Q(\sqrt{-10}) \).

Base change

This is a primitive isogeny class.

Twists

Below are some of the twists of this isogeny class.

Twist	Extension degree	Common base change
2.211.ah_aii	$2$	(not in LMFDB)
2.211.h_aii	$2$	(not in LMFDB)
2.211.bz_bou	$2$	(not in LMFDB)
2.211.aj_fg	$3$	(not in LMFDB)
2.211.ag_cs	$3$	(not in LMFDB)