Abelian variety isogeny class 2.181.abw_bju over $\F_{181}$

• Label: 2.181.abw_bju
• Base field: $\F_{181}$
• 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:	$\F_{181}$
Dimension:	$2$
L-polynomial:	$1 - 48 x + 930 x^{2} - 8688 x^{3} + 32761 x^{4}$
Frobenius angles:	$\pm0.0243701074205$, $\pm0.211718100097$
Angle rank:	$2$ (numerical)
Number field:	4.0.4672.2
Galois group:	$D_{4}$
Jacobians:	$22$

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$24956$	$1058833168$	$35145606897884$	$1151931946774930432$	$37738606348488341996156$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$134$	$32318$	$5927006$	$1073278734$	$194264293814$	$35161825531214$	$6364290799022990$	$1151936654839784350$	$208500535016148491750$	$37738596846313093815518$

Jacobians and polarizations

This isogeny class contains the Jacobians of 22 curves (of which all are hyperelliptic), and hence is principally polarizable:

• $y^2=54x^6+159x^5+67x^4+139x^3+180x^2+138x+174$
• $y^2=61x^6+161x^5+19x^4+77x^3+118x^2+49x+127$
• $y^2=44x^6+128x^5+37x^4+75x^3+20x^2+167x+116$
• $y^2=156x^6+39x^5+44x^4+170x^3+38x^2+114x+99$
• $y^2=76x^6+115x^5+81x^4+125x^3+132x^2+106x+173$
• $y^2=35x^6+16x^5+118x^4+x^3+14x^2+37x+92$
• $y^2=105x^6+63x^5+114x^4+125x^3+62x^2+87x+17$
• $y^2=175x^6+159x^5+70x^4+110x^3+104x^2+x+58$
• $y^2=77x^6+173x^5+130x^4+92x^3+80x^2+140x+94$
• $y^2=172x^6+89x^5+26x^4+164x^3+39x^2+144x+80$
• $y^2=54x^6+128x^5+83x^4+130x^3+9x^2+42x+175$
• $y^2=85x^6+149x^5+101x^4+93x^3+167x^2+95x+147$
• $y^2=153x^6+116x^5+35x^4+28x^3+153x^2+82x+112$
• $y^2=115x^6+27x^5+79x^4+143x^3+21x^2+18x+13$
• $y^2=147x^6+127x^5+91x^4+158x^3+45x^2+65x+35$
• $y^2=113x^5+6x^4+82x^3+43x^2+60x+143$
• $y^2=141x^6+171x^5+124x^4+76x^3+174x^2+25x+168$
• $y^2=15x^6+147x^5+175x^4+110x^3+65x^2+121x+129$
• $y^2=18x^6+175x^5+38x^4+19x^3+97x^2+66x+180$
• $y^2=40x^6+20x^5+94x^4+38x^3+114x^2+100x+23$
• $y^2=2x^6+86x^5+3x^4+133x^3+6x^2+151x+134$
• $y^2=84x^6+100x^5+167x^4+173x^3+143x^2+75x+66$

Decomposition and endomorphism algebra

All geometric endomorphisms are defined over $\F_{181}$.

Endomorphism algebra over $\F_{181}$

The endomorphism algebra of this simple isogeny class is 4.0.4672.2.

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
2.181.bw_bju	$2$	(not in LMFDB)