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

• Label: 2.181.abu_bia
• 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:	$1 - 46 x + 884 x^{2} - 8326 x^{3} + 32761 x^{4}$
Frobenius angles:	$\pm0.0978554663067$, $\pm0.226927340693$
Angle rank:	$2$ (numerical)
Number field:	4.0.16097088.1
Galois group:	$D_{4}$
Jacobians:	$32$

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$25274$	$1061962932$	$35159923103354$	$1151980521528452688$	$37738747233877331169434$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$136$	$32414$	$5929420$	$1073323990$	$194265019036$	$35161836529790$	$6364290971007784$	$1151936657693951518$	$208500535064304087304$	$37738596847085748459374$

Jacobians and polarizations

This isogeny class contains the Jacobians of 32 curves (of which all are hyperelliptic), and hence is principally polarizable:

• $y^2=27x^6+107x^5+180x^4+74x^3+79x^2+26x+76$
• $y^2=15x^6+133x^5+98x^4+146x^3+22x^2+20x+65$
• $y^2=20x^6+116x^5+113x^4+98x^3+89x^2+147x+133$
• $y^2=121x^6+26x^5+83x^4+152x^3+87x^2+65x+149$
• $y^2=177x^6+161x^5+55x^4+129x^3+176x^2+122x+145$
• $y^2=155x^6+42x^5+146x^4+3x^3+99x^2+22x+105$
• $y^2=64x^6+91x^5+131x^4+108x^3+86x^2+158x+110$
• $y^2=98x^6+167x^5+110x^4+73x^3+52x^2+151x+65$
• $y^2=17x^6+23x^5+55x^4+66x^3+111x^2+47x+65$
• $y^2=175x^6+38x^5+139x^4+20x^3+110x^2+81x+53$
• $y^2=80x^6+14x^5+120x^4+115x^3+16x^2+102x+150$
• $y^2=98x^6+31x^5+26x^4+5x^3+162x^2+158x+95$
• $y^2=158x^6+118x^5+56x^4+176x^3+110x^2+9x+120$
• $y^2=150x^6+54x^5+60x^4+128x^3+141x^2+8x+134$
• $y^2=120x^6+122x^5+142x^4+16x^3+154x^2+43x+98$
• $y^2=124x^6+29x^5+60x^4+29x^3+105x^2+103x+32$
• $y^2=90x^6+98x^5+61x^4+93x^3+143x^2+65x+132$
• $y^2=159x^6+156x^5+40x^4+123x^3+4x^2+82x+27$
• $y^2=147x^6+151x^5+142x^4+163x^3+9x^2+76x+90$
• $y^2=118x^6+33x^5+24x^4+161x^3+137x^2+173x+164$
• and

• $y^2=41x^6+60x^5+90x^4+20x^3+177x^2+146x+31$
• $y^2=83x^6+121x^5+78x^4+29x^3+5x^2+62x+46$
• $y^2=148x^6+x^5+164x^4+25x^3+92x^2+158x+32$
• $y^2=128x^6+78x^5+19x^4+3x^3+82x^2+84x+133$
• $y^2=92x^6+66x^5+14x^4+53x^3+17x^2+63x+153$
• $y^2=44x^6+152x^5+11x^4+110x^3+132x^2+153x+51$
• $y^2=96x^6+135x^5+37x^4+148x^3+66x^2+55x+112$
• $y^2=55x^6+53x^5+52x^4+55x^3+115x^2+147x+40$
• $y^2=173x^6+x^5+71x^4+30x^3+41x^2+166x+170$
• $y^2=130x^6+159x^5+21x^4+83x^3+19x^2+92x+79$
• $y^2=146x^6+53x^5+24x^4+169x^3+176x^2+68x+114$
• $y^2=177x^6+115x^5+61x^4+85x^3+45x^2+62x+14$

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 4.0.16097088.1.

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_bia	$2$	(not in LMFDB)