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

• Label: 2.181.abu_bie
• 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:	$1 - 46 x + 888 x^{2} - 8326 x^{3} + 32761 x^{4}$
Frobenius angles:	$\pm0.128869422289$, $\pm0.209863845130$
Angle rank:	$2$ (numerical)
Number field:	4.0.4394304.1
Galois group:	$D_{4}$
Jacobians:	$24$

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$25278$	$1062232116$	$35163200751822$	$1152001645299224016$	$37738841063867831322798$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$136$	$32422$	$5929972$	$1073343670$	$194265502036$	$35161845442342$	$6364291094756248$	$1151936658815945374$	$208500535064234289112$	$37738596846825070990102$

Jacobians and polarizations

This isogeny class contains the Jacobians of 24 curves (of which all are hyperelliptic), and hence is principally polarizable:

• $y^2=21x^6+61x^5+150x^4+152x^3+171x^2+63x+21$
• $y^2=179x^6+160x^5+107x^4+154x^3+106x^2+9x+104$
• $y^2=61x^6+166x^5+140x^4+23x^3+121x^2+52x+48$
• $y^2=58x^6+124x^5+123x^4+165x^3+170x^2+152x+15$
• $y^2=75x^6+108x^5+120x^4+11x^3+136x^2+65x+2$
• $y^2=73x^6+92x^5+167x^4+125x^3+142x^2+105x+119$
• $y^2=92x^6+137x^5+20x^4+20x^3+152x^2+89$
• $y^2=43x^6+118x^5+48x^4+144x^3+33x^2+10x+78$
• $y^2=50x^6+93x^5+37x^4+140x^3+78x^2+68x+100$
• $y^2=178x^6+56x^5+45x^4+9x^3+93x^2+17x+70$
• $y^2=98x^6+87x^4+80x^3+10x^2+101x+173$
• $y^2=48x^6+74x^5+85x^4+2x^3+69x^2+129x+174$
• $y^2=55x^6+58x^5+175x^4+152x^3+115x^2+180x+175$
• $y^2=113x^6+3x^5+58x^4+105x^3+135x^2+29x+17$
• $y^2=94x^6+155x^5+76x^4+163x^3+166x^2+171x+155$
• $y^2=138x^6+109x^5+45x^4+118x^3+143x^2+166x+22$
• $y^2=32x^6+88x^5+172x^4+131x^3+97x^2+144x+43$
• $y^2=29x^6+12x^5+136x^4+66x^3+69x^2+42x+29$
• $y^2=131x^6+170x^5+19x^4+139x^3+38x^2+111x+43$
• $y^2=150x^6+174x^5+13x^4+56x^3+13x^2+153x+101$
• $y^2=22x^6+109x^5+81x^4+97x^3+62x^2+73x+84$
• $y^2=167x^6+100x^5+176x^4+18x^3+73x^2+161x+121$
• $y^2=29x^6+43x^5+98x^4+146x^3+177x^2+169x+62$
• $y^2=174x^6+161x^5+158x^4+56x^3+119x^2+65x+50$

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 4.0.4394304.1.

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_bie	$2$	(not in LMFDB)