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

• Label: 2.181.abw_bka
• 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:	$1 - 48 x + 936 x^{2} - 8688 x^{3} + 32761 x^{4}$
Frobenius angles:	$\pm0.106535498304$, $\pm0.182910012524$
Angle rank:	$2$ (numerical)
Number field:	4.0.1069312.2
Galois group:	$D_{4}$
Jacobians:	$20$

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$24962$	$1059237508$	$35150737767698$	$1151967265054901008$	$37738779508651095468482$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$134$	$32330$	$5927870$	$1073311638$	$194265185174$	$35161844657978$	$6364291140065678$	$1151936659990125214$	$208500535081889449958$	$37738596847002210016490$

Jacobians and polarizations

This isogeny class contains the Jacobians of 20 curves (of which all are hyperelliptic), and hence is principally polarizable:

• $y^2=57x^6+114x^5+32x^4+143x^3+177x^2+87x+11$
• $y^2=146x^6+168x^5+111x^4+43x^3+34x^2+152x+167$
• $y^2=12x^6+101x^5+136x^4+178x^3+14x^2+167x+62$
• $y^2=100x^6+22x^5+36x^4+76x^3+26x^2+179x+41$
• $y^2=40x^6+56x^5+50x^4+109x^3+34x^2+10x+5$
• $y^2=24x^6+100x^5+95x^4+115x^3+98x^2+149x+125$
• $y^2=15x^6+51x^5+155x^3+26x^2+38x+39$
• $y^2=146x^6+75x^5+179x^4+102x^3+48x^2+44x+86$
• $y^2=168x^6+28x^5+115x^4+147x^3+165x^2+92x+40$
• $y^2=41x^6+115x^5+129x^4+130x^3+128x^2+81x+159$
• $y^2=160x^6+170x^5+158x^4+5x^3+49x^2+108x+113$
• $y^2=177x^6+113x^5+69x^4+68x^3+124x^2+97x+21$
• $y^2=54x^6+59x^5+157x^4+125x^3+160x^2+165x+71$
• $y^2=138x^6+37x^5+70x^4+140x^3+20x^2+148x+78$
• $y^2=25x^6+97x^5+59x^4+80x^3+119x^2+52x+118$
• $y^2=123x^6+179x^5+179x^4+167x^3+12x^2+146x+127$
• $y^2=77x^6+171x^5+61x^4+20x^3+38x^2+51x+88$
• $y^2=x^6+7x^5+27x^4+111x^3+74x^2+115x+10$
• $y^2=85x^6+77x^5+20x^4+11x^3+176x^2+24x+83$
• $y^2=67x^6+41x^5+61x^4+82x^3+71x^2+111x+120$

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 4.0.1069312.2.

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.bw_bka	$2$	(not in LMFDB)