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

• Label: 2.181.abx_bkw
• 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:	$1 - 49 x + 958 x^{2} - 8869 x^{3} + 32761 x^{4}$
Frobenius angles:	$\pm0.0510791052243$, $\pm0.186092366958$
Angle rank:	$2$ (numerical)
Number field:	4.0.1177964.1
Galois group:	$D_{4}$
Jacobians:	$10$

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$24802$	$1057507676$	$35141497343992$	$1151929169285599616$	$37738645003174932161962$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$133$	$32277$	$5926312$	$1073276145$	$194264492793$	$35161832626122$	$6364290950866261$	$1151936657291704449$	$208500535047331945432$	$37738596846616843872877$

Jacobians and polarizations

This isogeny class contains the Jacobians of 10 curves (of which all are hyperelliptic), and hence is principally polarizable:

• $y^2=28x^6+26x^5+109x^4+119x^3+6x^2+22x+82$
• $y^2=136x^6+114x^5+49x^4+5x^3+179x^2+79x+100$
• $y^2=2x^6+x^5+170x^4+35x^3+155x^2+15x+64$
• $y^2=54x^6+84x^5+17x^4+100x^3+142x^2+40x+17$
• $y^2=97x^6+124x^5+64x^4+50x^3+173x^2+95x+147$
• $y^2=3x^6+92x^5+168x^4+152x^3+173x^2+22x+16$
• $y^2=126x^6+99x^5+148x^4+75x^3+18x^2+72x+32$
• $y^2=108x^6+94x^4+56x^3+134x^2+83x+120$
• $y^2=160x^6+12x^5+163x^4+156x^3+5x^2+63x+147$
• $y^2=140x^6+77x^5+153x^4+64x^3+102x^2+115x+8$

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 4.0.1177964.1.

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.bx_bkw	$2$	(not in LMFDB)