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

• Label: 2.181.aca_bny
• Base field: $\F_{181}$
• Dimension: $2$
• $p$-rank: $2$
• Ordinary: yes
• Supersingular: no
• Simple: no
• Geometrically simple: no
• Primitive: yes
• Principally polarizable: yes
• Contains a Jacobian: yes

Invariants

Base field:	$\F_{181}$
Dimension:	$2$
L-polynomial:	$( 1 - 26 x + 181 x^{2} )^{2}$
	$1 - 52 x + 1038 x^{2} - 9412 x^{3} + 32761 x^{4}$
Frobenius angles:	$\pm0.0828936782352$, $\pm0.0828936782352$
Angle rank:	$1$ (numerical)
Jacobians:	$8$

This isogeny class is not 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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$24336$	$1052872704$	$35120842048656$	$1151865665532002304$	$37738505921630646287376$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$130$	$32134$	$5922826$	$1073216974$	$194263776850$	$35161828130518$	$6364291006808410$	$1151936659928854174$	$208500535106383986466$	$37738596847623225142054$

Jacobians and polarizations

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

• $y^2=x^6+60x^3+67$
• $y^2=51x^6+143x^5+26x^4+66x^3+26x^2+143x+51$
• $y^2=x^6+180$
• $y^2=92x^6+114x^5+69x^4+16x^3+131x^2+48x+118$
• $y^2=40x^6+170x^4+170x^2+40$
• $y^2=107x^6+51x^5+165x^4+150x^3+165x^2+51x+107$
• $y^2=68x^6+131x^5+130x^4+81x^3+130x^2+131x+68$
• $y^2=69x^6+33x^4+33x^2+69$

Decomposition and endomorphism algebra

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

Endomorphism algebra over $\F_{181}$

The isogeny class factors as 1.181.aba^2 and its endomorphism algebra is $\mathrm{M}_{2}($\(\Q(\sqrt{-3}) \)$)$

Base change

This is a primitive isogeny class.

Twists

Below are some of the twists of this isogeny class.

Twist	Extension degree	Common base change
2.181.a_amc	$2$	(not in LMFDB)
2.181.ca_bny	$2$	(not in LMFDB)
2.181.at_gy	$3$	(not in LMFDB)
2.181.ah_afc	$3$	(not in LMFDB)
2.181.o_pv	$3$	(not in LMFDB)
2.181.ba_tb	$3$	(not in LMFDB)
2.181.bm_bbv	$3$	(not in LMFDB)