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

• Label: 2.211.acd_bth
• 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:	$1 - 55 x + 1177 x^{2} - 11605 x^{3} + 44521 x^{4}$
Frobenius angles:	$\pm0.0550665583693$, $\pm0.137529233499$
Angle rank:	$2$ (numerical)
Number field:	4.0.92525.1
Galois group:	$D_{4}$
Jacobians:	$5$

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$34039$	$1952443001$	$88180350653449$	$3928689259657766525$	$174913942390199623017904$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$157$	$43851$	$9386947$	$1982064843$	$418227082152$	$88245946113951$	$18619893437458057$	$3928797481423157283$	$828976267981778867947$	$174913992535859943488806$

Jacobians and polarizations

This isogeny class contains the Jacobians of 5 curves (of which all are hyperelliptic), and hence is principally polarizable:

• $y^2=100x^6+76x^5+36x^4+121x^3+8x^2+3x+172$
• $y^2=207x^6+172x^5+83x^4+95x^3+9x^2+30x+192$
• $y^2=128x^6+77x^5+119x^4+191x^3+91x^2+157x+32$
• $y^2=124x^6+94x^5+4x^4+191x^3+137x^2+143x+68$
• $y^2=68x^6+109x^5+181x^4+69x^3+42x^2+6x+206$

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 4.0.92525.1.

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.cd_bth	$2$	(not in LMFDB)