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

• Label: 2.181.abu_big
• 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:	$( 1 - 24 x + 181 x^{2} )( 1 - 22 x + 181 x^{2} )$
	$1 - 46 x + 890 x^{2} - 8326 x^{3} + 32761 x^{4}$
Frobenius angles:	$\pm0.149335043618$, $\pm0.195291079027$
Angle rank:	$2$ (numerical)
Jacobians:	$16$

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$25280$	$1062366720$	$35164839608000$	$1152012181462548480$	$37738887442719518072000$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$136$	$32426$	$5930248$	$1073353486$	$194265740776$	$35161849733978$	$6364291149864616$	$1151936659163311006$	$208500535058742351688$	$37738596846579535551626$

Jacobians and polarizations

This isogeny class contains the Jacobians of 16 curves (of which all are hyperelliptic), and hence is principally polarizable:

• $y^2=74x^6+72x^5+102x^4+59x^3+101x^2+85x+146$
• $y^2=51x^6+160x^5+75x^4+64x^3+75x^2+160x+51$
• $y^2=63x^6+3x^5+22x^4+171x^3+120x^2+x+131$
• $y^2=19x^6+39x^5+95x^4+53x^3+95x^2+39x+19$
• $y^2=71x^6+125x^5+56x^4+24x^3+178x^2+16x+159$
• $y^2=126x^6+135x^5+93x^4+163x^3+71x^2+177x+116$
• $y^2=77x^6+125x^5+63x^4+58x^3+98x^2+117x+157$
• $y^2=88x^6+165x^5+113x^4+16x^3+113x^2+165x+88$
• $y^2=40x^6+73x^5+94x^4+43x^3+20x^2+75x+51$
• $y^2=146x^6+15x^5+92x^4+29x^3+92x^2+15x+146$
• $y^2=112x^6+50x^5+146x^4+18x^3+146x^2+50x+112$
• $y^2=179x^6+179x^5+8x^4+98x^3+107x^2+123x+84$
• $y^2=26x^6+55x^4+5x^3+55x^2+26$
• $y^2=102x^6+78x^5+44x^4+43x^3+44x^2+78x+102$
• $y^2=164x^6+119x^5+7x^4+23x^3+92x^2+180x+109$
• $y^2=4x^6+85x^5+22x^4+95x^3+22x^2+85x+4$

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 $\times$ 1.181.aw 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.ay : \(\Q(\sqrt{-37}) \).
• 1.181.aw : \(\Q(\sqrt{-15}) \).

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.ac_agk	$2$	(not in LMFDB)
2.181.c_agk	$2$	(not in LMFDB)
2.181.bu_big	$2$	(not in LMFDB)