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

• Label: 2.211.aca_bqf
• 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:	$( 1 - 27 x + 211 x^{2} )( 1 - 25 x + 211 x^{2} )$
	$1 - 52 x + 1097 x^{2} - 10972 x^{3} + 44521 x^{4}$
Frobenius angles:	$\pm0.120343810545$, $\pm0.170129106792$
Angle rank:	$2$ (numerical)
Jacobians:	$24$

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$34595$	$1959564585$	$88223487616880$	$3928881971928659625$	$174914644949400563994875$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$160$	$44012$	$9391540$	$1982162068$	$418228762000$	$88245970450022$	$18619893727933840$	$3928797484003521508$	$828976267990326763660$	$174913992535584938393852$

Jacobians and polarizations

This isogeny class contains the Jacobians of 24 curves (of which all are hyperelliptic), and hence is principally polarizable:

• $y^2=x^6+49x^5+36x^4+106x^3+25x^2+x+203$
• $y^2=177x^6+129x^5+184x^4+108x^3+184x^2+129x+177$
• $y^2=7x^6+137x^5+136x^4+180x^3+121x^2+96x+110$
• $y^2=99x^6+64x^5+12x^4+20x^3+168x^2+95x+99$
• $y^2=48x^6+54x^5+17x^4+55x^3+190x^2+143x+145$
• $y^2=100x^6+106x^5+17x^4+9x^3+29x^2+142x+66$
• $y^2=127x^6+77x^5+205x^4+139x^3+23x^2+12x+31$
• $y^2=11x^6+114x^5+149x^4+81x^3+155x^2+185x+171$
• $y^2=206x^6+75x^5+136x^4+129x^3+13x^2+202x+140$
• $y^2=198x^6+146x^5+107x^4+78x^3+183x^2+186x+23$
• $y^2=169x^6+10x^5+66x^4+127x^3+201x^2+57x+113$
• $y^2=106x^6+32x^5+98x^4+198x^3+153x^2+41x+41$
• $y^2=85x^6+119x^5+13x^4+51x^3+58x^2+34x+164$
• $y^2=67x^6+25x^5+177x^4+176x^3+12x^2+44x+12$
• $y^2=74x^6+142x^5+66x^4+85x^3+119x^2+174x+177$
• $y^2=169x^6+50x^5+119x^4+35x^3+109x^2+153x+203$
• $y^2=42x^6+29x^5+129x^4+44x^3+142x^2+35x+147$
• $y^2=146x^6+127x^5+5x^4+210x^3+24x^2+124x+129$
• $y^2=203x^6+166x^5+118x^4+53x^3+140x^2+10x+109$
• $y^2=96x^6+53x^5+191x^4+108x^3+175x^2+62x+148$
• $y^2=140x^6+128x^5+157x^4+18x^3+68x^2+205x+146$
• $y^2=35x^6+35x^5+50x^4+148x^3+159x^2+102x+164$
• $y^2=198x^6+86x^5+47x^4+12x^3+95x^2+67x+210$
• $y^2=3x^6+209x^5+151x^4+22x^3+65x^2+194x+157$

Decomposition and endomorphism algebra

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

Endomorphism algebra over $\F_{211}$

The isogeny class factors as 1.211.abb $\times$ 1.211.az 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.abb : \(\Q(\sqrt{-115}) \).
• 1.211.az : \(\Q(\sqrt{-219}) \).

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.ac_ajt	$2$	(not in LMFDB)
2.211.c_ajt	$2$	(not in LMFDB)
2.211.ca_bqf	$2$	(not in LMFDB)