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

• Label: 2.181.abw_bkc
• Base field: $\F_{181}$
• Dimension: $2$
• $p$-rank: $2$
• Ordinary: yes
• Supersingular: no
• Simple: no
• Geometrically simple: no
• Primitive: yes
• Principally polarizable: yes
• Contains a Jacobian: yes

Invariants

Base field:	$\F_{181}$
Dimension:	$2$
L-polynomial:	$( 1 - 24 x + 181 x^{2} )^{2}$
	$1 - 48 x + 938 x^{2} - 8688 x^{3} + 32761 x^{4}$
Frobenius angles:	$\pm0.149335043618$, $\pm0.149335043618$
Angle rank:	$1$ (numerical)
Jacobians:	$13$

This isogeny class is not 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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$24964$	$1059372304$	$35152448102500$	$1151979003524911104$	$37738836482772472975684$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$134$	$32334$	$5928158$	$1073322574$	$194265478454$	$35161850791518$	$6364291243075214$	$1151936661338402974$	$208500535093238159078$	$37738596846971936211054$

Jacobians and polarizations

This isogeny class contains the Jacobians of 13 curves (of which all are hyperelliptic), and hence is principally polarizable:

• $y^2=81x^6+177x^5+95x^4+75x^3+136x^2+61x+58$
• $y^2=65x^6+9x^5+86x^4+171x^3+63x^2+153x+89$
• $y^2=164x^6+64x^5+7x^4+83x^3+65x^2+34x+6$
• $y^2=139x^6+78x^5+103x^4+43x^3+100x^2+16x+134$
• $y^2=6x^6+78x^5+70x^4+18x^3+70x^2+78x+6$
• $y^2=46x^6+48x^5+5x^4+151x^3+159x^2+171x+121$
• $y^2=158x^6+180x^5+162x^4+73x^3+169x^2+51x+147$
• $y^2=91x^6+46x^5+120x^4+87x^3+120x^2+46x+91$
• $y^2=35x^6+126x^5+154x^4+29x^3+7x^2+50x+32$
• $y^2=122x^6+48x^5+114x^4+164x^3+117x^2+133x+2$
• $y^2=96x^6+112x^5+116x^4+30x^3+93x^2+x+47$
• $y^2=15x^6+114x^4+114x^2+15$
• $y^2=58x^6+50x^5+171x^4+48x^3+168x^2+138x+177$

Decomposition and endomorphism algebra

All geometric endomorphisms are defined over $\F_{181}$.

Endomorphism algebra over $\F_{181}$

The isogeny class factors as 1.181.ay^2 and its endomorphism algebra is $\mathrm{M}_{2}($\(\Q(\sqrt{-37}) \)$)$

Base change

This is a primitive isogeny class.

Twists

Below are some of the twists of this isogeny class.

Twist	Extension degree	Common base change
2.181.a_aig	$2$	(not in LMFDB)
2.181.bw_bkc	$2$	(not in LMFDB)
2.181.y_pf	$3$	(not in LMFDB)