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

• Label: 2.181.abx_bkv
• 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:	$1 - 49 x + 957 x^{2} - 8869 x^{3} + 32761 x^{4}$
Frobenius angles:	$\pm0.0295624989655$, $\pm0.190960746979$
Angle rank:	$2$ (numerical)
Number field:	4.0.633717.2
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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$24801$	$1057440237$	$35140624323525$	$1151922971588050725$	$37738613257322806255056$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$133$	$32275$	$5926165$	$1073270371$	$194264329378$	$35161828899307$	$6364290878494633$	$1151936656056190051$	$208500535028375569105$	$37738596846350067133030$

Jacobians and polarizations

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

• $y^2=180x^6+150x^5+34x^4+137x^3+176x^2+64x+124$
• $y^2=87x^6+63x^5+164x^4+110x^3+4x^2+164x+78$
• $y^2=142x^6+140x^5+2x^4+60x^3+91x^2+144x+119$
• $y^2=58x^6+50x^5+180x^4+32x^3+82x^2+98x+170$
• $y^2=18x^6+143x^5+89x^4+155x^3+149x^2+144x+165$
• $y^2=30x^6+115x^5+76x^4+90x^3+32x^2+89x+61$
• $y^2=35x^6+166x^5+41x^4+84x^3+60x^2+145x+30$
• $y^2=161x^6+26x^5+123x^4+32x^3+50x^2+94x+85$

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 4.0.633717.2.

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.bx_bkv	$2$	(not in LMFDB)