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

• Label: 2.181.abu_bhw
• 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:	$1 - 46 x + 880 x^{2} - 8326 x^{3} + 32761 x^{4}$
Frobenius angles:	$\pm0.0668164501626$, $\pm0.238808050794$
Angle rank:	$2$ (numerical)
Number field:	4.0.20482880.1
Galois group:	$D_{4}$
Jacobians:	$36$

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$25270$	$1061693780$	$35156645539750$	$1151959329164384720$	$37738651974168818191750$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$136$	$32406$	$5928868$	$1073304246$	$194264528676$	$35161827177558$	$6364290829113976$	$1151936655993707166$	$208500535049332622968$	$37738596847017738560326$

Jacobians and polarizations

This isogeny class contains the Jacobians of 36 curves (of which all are hyperelliptic), and hence is principally polarizable:

• $y^2=86x^6+28x^5+93x^4+150x^3+16x^2+161x+44$
• $y^2=121x^6+150x^5+51x^4+45x^3+130x^2+13x+109$
• $y^2=151x^6+170x^5+31x^4+156x^3+10x^2+73x+129$
• $y^2=22x^6+150x^5+180x^4+161x^3+130x^2+23x+53$
• $y^2=97x^6+5x^5+99x^4+152x^3+13x^2+55x+4$
• $y^2=131x^6+92x^5+61x^4+164x^3+156x^2+147x+77$
• $y^2=164x^6+102x^5+35x^4+13x^3+103x^2+174x+163$
• $y^2=157x^6+154x^5+55x^4+61x^3+90x+104$
• $y^2=128x^6+72x^5+142x^4+135x^3+77x^2+135x+150$
• $y^2=103x^6+55x^5+67x^4+136x^3+159x^2+130x+152$
• $y^2=53x^6+130x^5+130x^4+138x^3+53x^2+111x+53$
• $y^2=136x^6+135x^5+154x^4+70x^3+8x^2+100x+41$
• $y^2=20x^6+92x^5+73x^4+76x^3+115x^2+143x+122$
• $y^2=179x^6+95x^5+172x^4+81x^3+14x^2+135x+98$
• $y^2=69x^6+91x^5+156x^4+177x^3+65x^2+85x+44$
• $y^2=47x^6+28x^5+86x^4+151x^3+145x^2+97x+79$
• $y^2=66x^6+43x^5+97x^4+158x^3+155x^2+131x+23$
• $y^2=100x^6+164x^5+94x^4+12x^3+95x^2+144x+131$
• $y^2=68x^6+65x^5+97x^4+57x^3+99x^2+31x+9$
• $y^2=168x^6+39x^5+19x^4+132x^3+25x^2+23x+6$
• and

• $y^2=9x^6+39x^5+93x^4+11x^3+93x^2+8x+26$
• $y^2=76x^6+153x^5+62x^4+169x^3+69x^2+147x+50$
• $y^2=56x^6+34x^5+105x^4+25x^3+126x^2+71x+118$
• $y^2=22x^6+139x^5+24x^4+102x^3+172x^2+130x+145$
• $y^2=8x^6+84x^5+59x^4+60x^3+47x^2+88x+143$
• $y^2=124x^6+71x^5+129x^4+113x^3+75x^2+78x+118$
• $y^2=57x^6+141x^5+25x^4+27x^3+97x^2+129x+30$
• $y^2=116x^6+137x^5+108x^4+145x^3+50x^2+114x+150$
• $y^2=156x^6+97x^5+67x^4+29x^3+55x^2+159x+35$
• $y^2=141x^6+107x^5+64x^4+146x^3+82x^2+72x+161$
• $y^2=90x^6+13x^5+154x^4+5x^3+158x^2+162x+59$
• $y^2=49x^6+94x^5+135x^4+36x^3+54x^2+82x+63$
• $y^2=171x^6+99x^5+28x^4+27x^3+94x^2+145x+76$
• $y^2=114x^6+64x^5+26x^4+132x^3+100x^2+46x+130$
• $y^2=125x^6+109x^5+28x^4+64x^3+32x^2+15x+133$
• $y^2=89x^6+45x^5+70x^4+167x^3+94x^2+65x+120$

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 4.0.20482880.1.

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_bhw	$2$	(not in LMFDB)