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

• Label: 2.181.abx_bky
• 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:	$( 1 - 26 x + 181 x^{2} )( 1 - 23 x + 181 x^{2} )$
	$1 - 49 x + 960 x^{2} - 8869 x^{3} + 32761 x^{4}$
Frobenius angles:	$\pm0.0828936782352$, $\pm0.173686936480$
Angle rank:	$2$ (numerical)
Jacobians:	$20$

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$24804$	$1057642560$	$35143243402176$	$1151941551823146240$	$37738708209327963498804$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$133$	$32281$	$5926606$	$1073287681$	$194264818153$	$35161839984598$	$6364291091271253$	$1151936659606500961$	$208500535080524057686$	$37738596847026297156001$

Jacobians and polarizations

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

• $y^2=93x^6+112x^5+161x^4+22x^3+65x^2+32x+72$
• $y^2=15x^6+65x^5+40x^4+47x^3+176x^2+43x+10$
• $y^2=146x^6+148x^5+86x^4+41x^3+23x^2+157x+51$
• $y^2=156x^6+98x^5+71x^4+140x^3+32x^2+26x+127$
• $y^2=46x^6+4x^5+77x^4+75x^3+164x^2+75x+51$
• $y^2=54x^6+155x^5+138x^4+151x^3+124x^2+56x+63$
• $y^2=158x^6+54x^5+95x^4+65x^3+64x^2+x+124$
• $y^2=80x^6+161x^5+57x^4+149x^3+145x^2+31x+106$
• $y^2=91x^6+39x^5+101x^4+6x^3+117x^2+32x+28$
• $y^2=32x^6+137x^5+134x^4+72x^3+45x^2+22$
• $y^2=168x^6+149x^5+157x^4+112x^3+24x^2+121x+10$
• $y^2=134x^6+120x^5+74x^4+66x^3+108x^2+117x+114$
• $y^2=135x^6+139x^5+27x^4+38x^3+69x^2+127x+6$
• $y^2=40x^6+174x^5+147x^4+6x^3+102x^2+151x+140$
• $y^2=49x^6+157x^5+87x^4+121x^3+176x^2+16x+137$
• $y^2=158x^6+64x^5+34x^4+39x^3+114x^2+12x+128$
• $y^2=152x^6+117x^5+165x^4+62x^3+138x^2+142x+105$
• $y^2=164x^6+151x^5+112x^4+76x^3+x^2+121x+12$
• $y^2=101x^6+71x^5+96x^4+104x^3+86x^2+138x+58$
• $y^2=146x^6+114x^5+170x^4+66x^3+115x^2+76x+48$

Decomposition and endomorphism algebra

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

Endomorphism algebra over $\F_{181}$

The isogeny class factors as 1.181.aba $\times$ 1.181.ax and its endomorphism algebra is a direct product of the endomorphism algebras for each isotypic factor. The endomorphism algebra for each factor is:

• 1.181.aba : \(\Q(\sqrt{-3}) \).
• 1.181.ax : \(\Q(\sqrt{-195}) \).

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.ad_ajc	$2$	(not in LMFDB)
2.181.d_ajc	$2$	(not in LMFDB)
2.181.bx_bky	$2$	(not in LMFDB)
2.181.aq_ht	$3$	(not in LMFDB)
2.181.ae_acx	$3$	(not in LMFDB)