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

• Label: 2.211.acd_btg
• 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:	$( 1 - 29 x + 211 x^{2} )( 1 - 26 x + 211 x^{2} )$
	$1 - 55 x + 1176 x^{2} - 11605 x^{3} + 44521 x^{4}$
Frobenius angles:	$\pm0.0189887838440$, $\pm0.147206137144$
Angle rank:	$2$ (numerical)
Jacobians:	$2$

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$34038$	$1952351604$	$88178798550600$	$3928674602701858464$	$174913840833702570036378$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$157$	$43849$	$9386782$	$1982057449$	$418226839327$	$88245939573538$	$18619893284716237$	$3928797478231568209$	$828976267920950113642$	$174913992534789320663929$

Jacobians and polarizations

This isogeny class contains the Jacobians of 2 curves (of which all are hyperelliptic), and hence is principally polarizable:

• $y^2=153x^6+144x^5+105x^4+172x^3+115x^2+174x+84$
• $y^2=110x^6+64x^5+144x^4+174x^3+73x^2+39x+176$

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.aba 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.aba : \(\Q(\sqrt{-42}) \).

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.ad_amu	$2$	(not in LMFDB)
2.211.d_amu	$2$	(not in LMFDB)
2.211.cd_btg	$2$	(not in LMFDB)
2.211.an_dg	$3$	(not in LMFDB)
2.211.ak_g	$3$	(not in LMFDB)