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

• Label: 2.181.aby_blz
• 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:	$( 1 - 25 x + 181 x^{2} )^{2}$
	$1 - 50 x + 987 x^{2} - 9050 x^{3} + 32761 x^{4}$
Frobenius angles:	$\pm0.120568372405$, $\pm0.120568372405$
Angle rank:	$1$ (numerical)
Jacobians:	$16$

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$24649$	$1056185001$	$35137532446864$	$1151928831456275625$	$37738705586833646899729$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$132$	$32236$	$5925642$	$1073275828$	$194264804652$	$35161843641046$	$6364291208736012$	$1151936662090031908$	$208500535121759180322$	$37738596847576101448156$

Jacobians and polarizations

This isogeny class contains the Jacobians of 16 curves (of which all are hyperelliptic), and hence is principally polarizable:

• $y^2=2x^6+2x^3+63$
• $y^2=29x^6+136x^5+143x^4+8x^3+62x^2+167x+49$
• $y^2=78x^6+112x^5+8x^4+17x^3+90x^2+57x+66$
• $y^2=67x^6+65x^5+58x^4+115x^3+19x^2+25x+1$
• $y^2=2x^6+2x^3+98$
• $y^2=155x^6+167x^5+180x^4+170x^3+143x^2+56x+151$
• $y^2=40x^6+30x^5+121x^4+106x^3+177x^2+157x+22$
• $y^2=113x^6+111x^5+83x^4+57x^3+83x^2+111x+113$
• $y^2=7x^6+80x^5+48x^4+160x^3+170x^2+92x+119$
• $y^2=180x^6+128x^5+100x^4+73x^3+80x^2+24x+27$
• $y^2=153x^6+27x^5+15x^4+133x^3+82x^2+177x+41$
• $y^2=2x^6+40x^3+72$
• $y^2=60x^6+12x^5+84x^4+31x^3+104x^2+78x+43$
• $y^2=35x^6+106x^5+161x^4+157x^3+75x^2+177x+20$
• $y^2=107x^6+10x^5+82x^4+56x^3+36x^2+118x+74$
• $y^2=66x^6+131x^5+83x^4+179x^3+123x^2+129x+69$

Decomposition and endomorphism algebra

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

Endomorphism algebra over $\F_{181}$

The isogeny class factors as 1.181.az^2 and its endomorphism algebra is $\mathrm{M}_{2}($\(\Q(\sqrt{-11}) \)$)$

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_akd	$2$	(not in LMFDB)
2.181.by_blz	$2$	(not in LMFDB)
2.181.z_rc	$3$	(not in LMFDB)