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

• Label: 2.181.aby_blw
• 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:	$1 - 50 x + 984 x^{2} - 9050 x^{3} + 32761 x^{4}$
Frobenius angles:	$\pm0.0363437804091$, $\pm0.167479033802$
Angle rank:	$2$ (numerical)
Number field:	4.0.247104.2
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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$24646$	$1055982516$	$35134859689414$	$1151909323634990544$	$37738602140474545196326$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$132$	$32230$	$5925192$	$1073257654$	$194264272152$	$35161831001446$	$6364290952683012$	$1151936657546963614$	$208500535050463373172$	$37738596846591296171350$

Jacobians and polarizations

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

• $y^2=93x^6+140x^5+20x^4+70x^3+95x^2+178x+179$
• $y^2=89x^6+96x^5+141x^4+145x^3+56x^2+105x+85$
• $y^2=110x^6+162x^5+14x^4+25x^3+74x^2+165x$
• $y^2=175x^6+123x^5+44x^4+110x^3+73x^2+54x+166$
• $y^2=66x^6+147x^5+69x^4+22x^3+84x^2+102x+135$
• $y^2=179x^6+61x^5+150x^4+50x^3+56x^2+163x+43$
• $y^2=151x^6+142x^5+64x^4+70x^3+92x^2+145x+178$
• $y^2=106x^6+99x^5+39x^4+129x^3+3x^2+174x+31$

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 4.0.247104.2.

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.by_blw	$2$	(not in LMFDB)