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

• Label: 2.211.aca_bqe
• 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:	$1 - 52 x + 1096 x^{2} - 10972 x^{3} + 44521 x^{4}$
Frobenius angles:	$\pm0.107380828994$, $\pm0.178838404908$
Angle rank:	$2$ (numerical)
Number field:	4.0.28928.2
Galois group:	$D_{4}$
Jacobians:	$28$

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$34594$	$1959473348$	$88222020401746$	$3928869226059576848$	$174914566439504376341794$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$160$	$44010$	$9391384$	$1982155638$	$418228574280$	$88245966155898$	$18619893648335776$	$3928797482828205534$	$828976267978157586016$	$174913992535563729569290$

Jacobians and polarizations

This isogeny class contains the Jacobians of 28 curves (of which all are hyperelliptic), and hence is principally polarizable:

• $y^2=88x^6+19x^5+15x^4+201x^3+145x^2+23x+203$
• $y^2=122x^6+164x^5+122x^4+62x^3+62x^2+144x+121$
• $y^2=156x^6+200x^5+12x^4+193x^3+65x^2+111x+27$
• $y^2=188x^6+111x^4+114x^3+115x^2+201x+157$
• $y^2=59x^6+190x^5+26x^4+132x^3+107x^2+66x+33$
• $y^2=30x^6+161x^5+153x^4+89x^3+157x^2+120x+42$
• $y^2=173x^6+152x^5+7x^4+36x^3+57x^2+33x+119$
• $y^2=166x^6+184x^5+17x^4+173x^3+207x^2+120x+141$
• $y^2=42x^6+95x^5+43x^4+114x^3+68x^2+79x+91$
• $y^2=17x^6+163x^5+142x^4+167x^3+128x^2+167x+178$
• $y^2=16x^6+142x^5+201x^4+86x^3+151x^2+58x+105$
• $y^2=33x^6+84x^5+151x^4+131x^3+63x^2+160x+74$
• $y^2=108x^6+87x^5+199x^4+9x^3+106x^2+201x+7$
• $y^2=100x^6+153x^5+62x^4+171x^3+27x^2+113x+203$
• $y^2=127x^6+15x^5+34x^4+142x^3+71x^2+118x+65$
• $y^2=79x^6+79x^5+30x^4+120x^3+173x^2+87x+19$
• $y^2=98x^6+41x^5+151x^4+145x^3+143x^2+179x+127$
• $y^2=48x^6+197x^5+188x^4+145x^3+154x^2+15x+64$
• $y^2=79x^6+95x^5+209x^3+16x^2+80x+157$
• $y^2=73x^6+179x^5+155x^4+12x^3+174x^2+208x+27$
• $y^2=190x^6+9x^5+143x^4+20x^3+83x^2+37x+2$
• $y^2=6x^6+188x^5+174x^4+203x^3+128x^2+175x+10$
• $y^2=207x^6+83x^5+136x^4+18x^3+92x^2+158x+181$
• $y^2=18x^6+93x^5+43x^4+165x^3+88x^2+169x+67$
• $y^2=110x^6+200x^5+82x^4+50x^3+73x^2+39x+11$
• $y^2=30x^6+178x^5+23x^4+126x^3+92x^2+138x+26$
• $y^2=35x^6+24x^5+200x^4+71x^3+18x^2+200x+28$
• $y^2=198x^6+33x^5+32x^4+31x^3+122x^2+131x+49$

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 4.0.28928.2.

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.ca_bqe	$2$	(not in LMFDB)