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

• Label: 2.181.abv_bit
• 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:	$1 - 47 x + 903 x^{2} - 8507 x^{3} + 32761 x^{4}$
Frobenius angles:	$\pm0.0200095723598$, $\pm0.230670495285$
Angle rank:	$2$ (numerical)
Number field:	4.0.22725.1
Galois group:	$D_{4}$
Jacobians:	$8$

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$25111$	$1060161309$	$35149842960811$	$1151936802973792629$	$37738585744099234253776$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$135$	$32359$	$5927721$	$1073283259$	$194264187750$	$35161821527263$	$6364290726593865$	$1151936654044490419$	$208500535013615272671$	$37738596846419746934854$

Jacobians and polarizations

This isogeny class contains the Jacobians of 8 curves (of which all are hyperelliptic), and hence is principally polarizable:

• $y^2=141x^6+153x^5+166x^4+37x^3+140x^2+117x+157$
• $y^2=77x^6+139x^5+38x^4+171x^3+102x^2+124x+94$
• $y^2=179x^6+29x^5+62x^4+139x^3+143x^2+17x+163$
• $y^2=102x^6+10x^5+112x^4+93x^3+161x^2+135x+164$
• $y^2=100x^6+147x^5+116x^4+70x^3+161x^2+73x+81$
• $y^2=115x^6+136x^5+21x^4+116x^3+105x^2+61x+119$
• $y^2=159x^6+15x^5+137x^4+73x^3+109x^2+53x+125$
• $y^2=39x^6+104x^5+65x^4+167x^3+88x^2+176x+146$

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 4.0.22725.1.

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
2.181.bv_bit	$2$	(not in LMFDB)