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

• Label: 2.181.abu_bht
• 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:	$1 - 46 x + 877 x^{2} - 8326 x^{3} + 32761 x^{4}$
Frobenius angles:	$\pm0.0353322619336$, $\pm0.246093822352$
Angle rank:	$2$ (numerical)
Number field:	4.0.9837632.1
Galois group:	$D_{4}$
Jacobians:	$14$

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$25267$	$1061491937$	$35154187422508$	$1151943389876167625$	$37738579591133669710627$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$136$	$32400$	$5928454$	$1073289396$	$194264156076$	$35161819874382$	$6364290710711356$	$1151936654332856676$	$208500535027878840334$	$37738596846735380193280$

Jacobians and polarizations

This isogeny class contains the Jacobians of 14 curves (of which all are hyperelliptic), and hence is principally polarizable:

• $y^2=19x^6+174x^5+61x^4+5x^3+84x^2+119x+50$
• $y^2=83x^6+37x^5+56x^4+92x^3+36x^2+154x+54$
• $y^2=88x^6+3x^5+136x^4+64x^3+139x^2+127x+37$
• $y^2=74x^6+55x^5+88x^4+108x^3+40x^2+105x+25$
• $y^2=102x^6+40x^5+92x^4+93x^3+25x^2+157x+44$
• $y^2=85x^6+13x^5+2x^4+50x^3+94x^2+46x+160$
• $y^2=12x^6+129x^5+113x^4+23x^3+20x^2+47x+73$
• $y^2=8x^6+122x^5+163x^4+87x^3+105x^2+157x+72$
• $y^2=98x^6+57x^5+148x^4+123x^3+151x^2+62x+42$
• $y^2=135x^6+91x^5+111x^4+155x^3+9x^2+80x+28$
• $y^2=131x^6+2x^5+113x^4+97x^3+96x^2+10x+66$
• $y^2=173x^6+31x^5+119x^4+125x^3+177x^2+55x+4$
• $y^2=63x^6+174x^5+10x^4+171x^3+138x^2+130x+106$
• $y^2=91x^6+151x^5+76x^4+104x^3+147x^2+17x+22$

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 4.0.9837632.1.

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.bu_bht	$2$	(not in LMFDB)