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

• Label: 2.181.abu_bih
• 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:	$( 1 - 23 x + 181 x^{2} )^{2}$
	$1 - 46 x + 891 x^{2} - 8326 x^{3} + 32761 x^{4}$
Frobenius angles:	$\pm0.173686936480$, $\pm0.173686936480$
Angle rank:	$1$ (numerical)
Jacobians:	$40$

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$25281$	$1062434025$	$35165659044096$	$1152017443113770025$	$37738910498109592648041$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$136$	$32428$	$5930386$	$1073358388$	$194265859456$	$35161851838678$	$6364291175734096$	$1151936659284147748$	$208500535054664128906$	$37738596846429369169948$

Jacobians and polarizations

This isogeny class contains the Jacobians of 40 curves (of which all are hyperelliptic), and hence is principally polarizable:

• $y^2=x^6+14x^3+29$
• $y^2=65x^6+76x^5+110x^4+90x^3+127x^2+118x+73$
• $y^2=93x^6+126x^5+129x^4+95x^3+93x^2+50x+74$
• $y^2=125x^6+28x^5+109x^4+111x^3+116x^2+23x+180$
• $y^2=32x^6+23x^5+146x^4+127x^3+132x^2+53x+5$
• $y^2=24x^6+76x^5+30x^4+134x^3+123x^2+54x+28$
• $y^2=77x^6+86x^5+19x^4+113x^3+24x^2+104x+8$
• $y^2=176x^6+131x^5+12x^4+126x^3+94x^2+19x+36$
• $y^2=168x^6+127x^5+116x^4+52x^3+75x^2+146x+158$
• $y^2=40x^6+127x^5+63x^4+155x^3+134x^2+122x+89$
• $y^2=146x^6+59x^5+18x^4+145x^3+148x^2+113x+69$
• $y^2=171x^6+73x^5+133x^4+32x^3+7x^2+61x+159$
• $y^2=30x^6+31x^5+125x^4+145x^3+129x^2+120x+107$
• $y^2=100x^6+160x^5+177x^4+71x^3+126x^2+23x+11$
• $y^2=31x^6+164x^5+151x^4+62x^3+125x^2+81x+90$
• $y^2=85x^6+14x^5+7x^4+85x^3+174x^2+14x+96$
• $y^2=x^6+x^3+132$
• $y^2=131x^6+25x^5+140x^4+79x^3+27x^2+58x+133$
• $y^2=68x^6+9x^5+69x^4+121x^3+2x^2+129x+30$
• $y^2=173x^6+131x^5+66x^4+99x^3+77x^2+123x+175$
• and

• $y^2=59x^6+131x^5+20x^4+21x^3+27x^2+142x+136$
• $y^2=71x^6+22x^5+32x^4+88x^3+120x^2+151x+110$
• $y^2=83x^6+177x^5+94x^4+170x^3+82x^2+102x+85$
• $y^2=101x^6+144x^5+128x^4+81x^3+124x^2+121x+70$
• $y^2=146x^6+144x^5+120x^4+177x^3+46x^2+152x+49$
• $y^2=130x^6+164x^5+135x^4+46x^3+125x^2+47x+30$
• $y^2=113x^6+56x^5+120x^4+147x^3+168x^2+119x+109$
• $y^2=20x^6+133x^5+21x^4+154x^3+82x^2+100x+50$
• $y^2=42x^6+18x^5+151x^4+138x^3+151x^2+18x+42$
• $y^2=129x^6+69x^5+140x^4+30x^3+78x^2+131x+87$
• $y^2=171x^6+50x^5+30x^4+95x^3+110x^2+89x+164$
• $y^2=79x^6+52x^5+76x^4+111x^3+74x^2+122x+70$
• $y^2=152x^6+155x^5+56x^4+136x^3+154x^2+7x+152$
• $y^2=54x^6+148x^5+98x^4+115x^3+93x^2+117x+2$
• $y^2=75x^6+117x^5+54x^4+165x^3+92x^2+29x+37$
• $y^2=30x^6+169x^5+42x^4+71x^3+42x^2+169x+30$
• $y^2=26x^6+83x^5+169x^4+173x^3+106x^2+86x+7$
• $y^2=23x^6+155x^5+54x^4+18x^3+100x^2+40x+134$
• $y^2=173x^6+52x^5+112x^4+33x^3+87x^2+144x+127$
• $y^2=105x^6+7x^5+26x^4+174x^3+59x^2+126x+115$

Decomposition and endomorphism algebra

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

Endomorphism algebra over $\F_{181}$

The isogeny class factors as 1.181.ax^2 and its endomorphism algebra is $\mathrm{M}_{2}($\(\Q(\sqrt{-195}) \)$)$

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.a_agl	$2$	(not in LMFDB)
2.181.bu_bih	$2$	(not in LMFDB)
2.181.x_nk	$3$	(not in LMFDB)