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

• Label: 2.181.abz_bmx
• 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:	$1 - 51 x + 1011 x^{2} - 9231 x^{3} + 32761 x^{4}$
Frobenius angles:	$\pm0.0467121644153$, $\pm0.139008714891$
Angle rank:	$2$ (numerical)
Number field:	4.0.50125.1
Galois group:	$D_{4}$
Jacobians:	$4$

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$24491$	$1054460005$	$35128277447231$	$1151890423380452005$	$37738568154960421158416$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$131$	$32183$	$5924081$	$1073240043$	$194264097206$	$35161831059383$	$6364291003667441$	$1151936659008828403$	$208500535079258968451$	$37738596847047153800198$

Jacobians and polarizations

This isogeny class contains the Jacobians of 4 curves (of which all are hyperelliptic), and hence is principally polarizable:

• $y^2=17x^6+4x^5+101x^4+9x^3+130x^2+151x+166$
• $y^2=161x^6+25x^5+166x^4+14x^3+129x^2+151x+22$
• $y^2=135x^6+51x^5+156x^4+48x^3+40x^2+75x+64$
• $y^2=61x^6+88x^5+146x^4+56x^3+14x^2+152x+146$

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 4.0.50125.1.

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.bz_bmx	$2$	(not in LMFDB)