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

• Label: 2.211.abz_bpc
• 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:	$1 - 51 x + 1068 x^{2} - 10761 x^{3} + 44521 x^{4}$
Frobenius angles:	$\pm0.102391743820$, $\pm0.201205779872$
Angle rank:	$2$ (numerical)
Number field:	4.0.7183384.1
Galois group:	$D_{4}$
Jacobians:	$24$

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$34778$	$1961548756$	$88231578862232$	$3928892350719755296$	$174914553696419655266198$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$161$	$44057$	$9392402$	$1982167305$	$418228543811$	$88245961182722$	$18619893511732793$	$3928797480392786449$	$828976267948451976902$	$174913992535406218532777$

Jacobians and polarizations

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

• $y^2=10x^6+78x^5+3x^4+26x^3+121x^2+136x+79$
• $y^2=192x^6+140x^5+117x^4+101x^3+45x^2+131x+185$
• $y^2=161x^6+55x^5+193x^4+90x^3+162x^2+49x+7$
• $y^2=122x^6+61x^5+207x^4+15x^3+138x^2+80x+31$
• $y^2=33x^6+54x^5+91x^4+159x^3+5x^2+55x+74$
• $y^2=132x^6+187x^5+45x^4+71x^3+116x^2+139x+87$
• $y^2=194x^6+124x^5+10x^4+60x^3+189x^2+12x+146$
• $y^2=132x^6+105x^5+164x^4+49x^3+206x^2+48x+172$
• $y^2=168x^6+85x^5+158x^4+64x^3+111x^2+100x+145$
• $y^2=x^6+192x^5+194x^4+47x^3+182x^2+9x+155$
• $y^2=17x^6+121x^5+49x^4+112x^3+66x^2+54x+184$
• $y^2=175x^6+191x^5+32x^4+180x^3+65x^2+35x+147$
• $y^2=25x^6+179x^5+29x^4+143x^3+120x^2+97x+129$
• $y^2=87x^6+120x^5+83x^4+151x^3+107x^2+93x+38$
• $y^2=26x^6+74x^5+197x^4+99x^3+154x^2+49x+97$
• $y^2=120x^6+60x^5+187x^4+122x^3+135x^2+82x+72$
• $y^2=91x^6+158x^5+25x^4+156x^3+107x^2+147x+130$
• $y^2=115x^6+107x^5+161x^4+210x^3+140x^2+157x+40$
• $y^2=172x^6+130x^5+71x^4+165x^3+205x^2+65x+142$
• $y^2=80x^6+102x^5+43x^4+208x^3+120x^2+11x+9$
• $y^2=58x^6+33x^5+120x^4+56x^3+54x^2+208x+195$
• $y^2=146x^6+201x^5+13x^4+170x^3+157x^2+105x+65$
• $y^2=75x^6+52x^5+154x^4+42x^3+180x^2+178x+102$
• $y^2=150x^6+157x^5+49x^4+40x^3+41x^2+78x+182$

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 4.0.7183384.1.

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_bpc	$2$	(not in LMFDB)