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

• Label: 2.211.abz_boz
• 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:	$1 - 51 x + 1065 x^{2} - 10761 x^{3} + 44521 x^{4}$
Frobenius angles:	$\pm0.0776026146318$, $\pm0.212630171293$
Angle rank:	$2$ (numerical)
Number field:	4.0.10933.1
Galois group:	$D_{4}$
Jacobians:	$35$

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$34775$	$1961275225$	$88227262150625$	$3928855849823338525$	$174914336453944949810000$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$161$	$44051$	$9391943$	$1982148891$	$418228024376$	$88245949773863$	$18619893309386621$	$3928797477518386051$	$828976267918458924383$	$174913992535274303834726$

Jacobians and polarizations

This isogeny class contains the Jacobians of 35 curves (of which all are hyperelliptic), and hence is principally polarizable:

• $y^2=181x^6+197x^5+199x^4+14x^3+25x^2+139x+112$
• $y^2=107x^6+209x^5+133x^4+188x^3+71x^2+106x+31$
• $y^2=168x^6+169x^5+156x^4+196x^3+191x^2+38x+177$
• $y^2=88x^6+28x^5+31x^4+155x^3+5x^2+119x+17$
• $y^2=174x^6+59x^5+103x^4+185x^3+200x^2+190x+2$
• $y^2=209x^6+81x^5+31x^4+148x^3+15x^2+153x+156$
• $y^2=182x^6+199x^5+193x^4+21x^3+108x^2+113x+66$
• $y^2=48x^6+127x^5+47x^4+77x^3+172x^2+44x+195$
• $y^2=70x^6+13x^5+14x^4+209x^3+158x^2+146x+87$
• $y^2=175x^6+161x^5+51x^4+209x^3+99x^2+192x+206$
• $y^2=104x^6+129x^5+42x^4+192x^3+94x^2+27x+197$
• $y^2=135x^6+139x^5+151x^4+40x^2+71x+13$
• $y^2=72x^6+64x^5+208x^4+47x^3+151x^2+138x+85$
• $y^2=x^6+14x^5+25x^4+164x^3+154x^2+201x+185$
• $y^2=167x^6+180x^5+141x^4+145x^3+189x^2+171x+64$
• $y^2=65x^6+21x^5+184x^4+44x^3+52x^2+112x+30$
• $y^2=84x^6+63x^5+74x^4+58x^3+134x^2+68x+92$
• $y^2=164x^6+6x^5+12x^4+131x^3+49x^2+177x+180$
• $y^2=154x^6+24x^5+203x^4+35x^3+190x^2+200x+177$
• $y^2=54x^6+207x^5+21x^4+205x^3+140x^2+175x+110$
• and

• $y^2=176x^6+53x^5+135x^4+49x^3+202x^2+18x+145$
• $y^2=151x^6+40x^5+62x^4+120x^3+166x^2+86x+23$
• $y^2=193x^6+3x^5+111x^4+76x^3+167x^2+92x+30$
• $y^2=154x^6+6x^5+109x^4+112x^3+185x^2+196x+96$
• $y^2=131x^6+8x^5+53x^4+17x^3+44x^2+112x+210$
• $y^2=194x^6+56x^5+49x^4+24x^3+51x^2+113x+174$
• $y^2=128x^6+58x^5+188x^4+49x^3+129x^2+61x+74$
• $y^2=81x^6+102x^5+77x^4+12x^3+52x^2+193x+67$
• $y^2=38x^6+61x^5+27x^4+174x^3+109x^2+67x+167$
• $y^2=142x^6+70x^5+168x^4+94x^3+83x^2+195x+87$
• $y^2=77x^6+182x^5+209x^4+18x^3+195x^2+60x+32$
• $y^2=197x^6+208x^5+80x^4+32x^3+32x^2+62x+97$
• $y^2=146x^6+205x^5+170x^4+87x^3+75x^2+65x+146$
• $y^2=180x^6+195x^5+22x^4+200x^3+8x^2+177x+8$
• $y^2=160x^6+8x^5+119x^4+91x^3+148x^2+146x+205$

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 4.0.10933.1.

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.bz_boz	$2$	(not in LMFDB)