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

• Label: 2.181.abu_bhy
• 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:	$( 1 - 26 x + 181 x^{2} )( 1 - 20 x + 181 x^{2} )$
	$1 - 46 x + 882 x^{2} - 8326 x^{3} + 32761 x^{4}$
Frobenius angles:	$\pm0.0828936782352$, $\pm0.233262291643$
Angle rank:	$2$ (numerical)
Jacobians:	$100$

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$25272$	$1061828352$	$35158284310968$	$1151969933920665600$	$37738699782737963730552$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$136$	$32410$	$5929144$	$1073314126$	$194264774776$	$35161831908682$	$6364290902336776$	$1151936656916753566$	$208500535058735279464$	$37738596847094450100730$

Jacobians and polarizations

This isogeny class contains the Jacobians of 100 curves (of which all are hyperelliptic), and hence is principally polarizable:

• $y^2=126x^6+173x^5+155x^4+12x^3+171x^2+77x+87$
• $y^2=125x^6+97x^5+132x^4+50x^3+132x^2+97x+125$
• $y^2=113x^6+55x^5+83x^4+98x^3+131x^2+151x+24$
• $y^2=22x^6+47x^5+9x^4+12x^3+172x^2+15x+139$
• $y^2=2x^6+30x^5+38x^4+74x^3+141x^2+113x+140$
• $y^2=49x^6+150x^5+153x^4+155x^3+153x^2+150x+49$
• $y^2=19x^6+84x^5+36x^4+151x^3+63x^2+18x+119$
• $y^2=94x^6+129x^5+27x^4+143x^3+53x^2+111x+83$
• $y^2=161x^6+144x^5+75x^4+82x^3+150x^2+63x+95$
• $y^2=154x^6+71x^5+104x^4+94x^3+104x^2+71x+154$
• $y^2=47x^6+115x^5+119x^4+83x^3+139x^2+164x+76$
• $y^2=96x^6+23x^5+116x^4+128x^3+116x^2+23x+96$
• $y^2=175x^6+99x^5+174x^4+151x^3+179x^2+178x+174$
• $y^2=94x^6+32x^5+54x^4+89x^3+109x^2+35x+2$
• $y^2=67x^6+113x^5+56x^4+57x^3+142x^2+103x+154$
• $y^2=157x^6+9x^5+76x^4+66x^3+171x^2+177x+26$
• $y^2=71x^6+146x^5+52x^4+40x^3+76x^2+53x+123$
• $y^2=114x^6+3x^5+9x^4+20x^3+81x^2+62x+27$
• $y^2=25x^6+11x^5+166x^4+159x^3+134x^2+79x+66$
• $y^2=85x^6+14x^5+115x^4+x^3+29x^2+75x+34$
• and

• $y^2=30x^6+39x^5+85x^4+37x^3+118x^2+159x+137$
• $y^2=41x^6+173x^5+5x^4+46x^3+20x^2+41x+13$
• $y^2=63x^6+158x^5+168x^4+87x^3+47x^2+144x+6$
• $y^2=50x^6+15x^5+51x^4+112x^3+73x^2+35x+129$
• $y^2=54x^6+87x^5+110x^4+9x^3+x^2+167x+32$
• $y^2=50x^6+133x^5+x^4+77x^3+35x^2+4x+166$
• $y^2=61x^6+36x^5+109x^4+164x^3+109x^2+36x+61$
• $y^2=35x^6+108x^5+114x^4+95x^3+49x^2+53x+26$
• $y^2=97x^6+112x^5+157x^4+16x^3+162x^2+35x+98$
• $y^2=33x^6+177x^5+132x^4+98x^3+37x^2+82x+14$
• $y^2=52x^6+117x^5+139x^4+159x^3+139x^2+117x+52$
• $y^2=121x^6+6x^5+131x^4+13x^3+141x^2+22x+158$
• $y^2=38x^6+35x^5+170x^4+47x^3+24x^2+6x+157$
• $y^2=177x^6+71x^5+12x^4+173x^3+39x^2+15x+108$
• $y^2=130x^6+68x^5+179x^4+112x^3+53x^2+19x+91$
• $y^2=110x^6+124x^5+72x^4+53x^3+40x^2+92x+7$
• $y^2=152x^6+71x^5+132x^4+47x^3+143x^2+135x+36$
• $y^2=167x^6+154x^5+82x^4+145x^3+144x^2+27x+84$
• $y^2=72x^6+10x^5+11x^4+80x^3+26x^2+25x+132$
• $y^2=172x^6+79x^5+51x^4+94x^3+51x^2+79x+172$
• $y^2=92x^6+51x^5+109x^4+175x^3+64x^2+47x+135$
• $y^2=160x^6+179x^5+179x^4+124x^3+50x^2+116x+155$
• $y^2=34x^6+66x^5+52x^4+132x^3+137x^2+149x+65$
• $y^2=112x^6+72x^5+19x^4+112x^3+79x^2+93x+67$
• $y^2=50x^6+6x^5+142x^4+130x^3+80x^2+107x+131$
• $y^2=165x^6+3x^5+52x^4+108x^3+124x^2+166x+152$
• $y^2=77x^6+18x^5+121x^4+48x^3+119x^2+88x+149$
• $y^2=21x^6+109x^5+177x^4+155x^3+177x^2+109x+21$
• $y^2=159x^6+129x^5+102x^4+82x^3+178x^2+171x+12$
• $y^2=68x^6+30x^5+91x^4+27x^3+158x^2+130x+146$
• $y^2=109x^6+95x^5+79x^4+2x^3+165x^2+7x+96$
• $y^2=175x^6+152x^5+95x^4+25x^3+95x^2+152x+175$
• $y^2=155x^6+123x^5+5x^4+87x^3+172x^2+7x+129$
• $y^2=161x^6+3x^5+3x^4+173x^3+25x^2+44x+96$
• $y^2=169x^6+70x^5+22x^4+80x^3+110x^2+121x+129$
• $y^2=77x^6+109x^5+86x^4+90x^3+125x^2+21x+104$
• $y^2=104x^6+100x^5+84x^4+45x^3+7x^2+75x+20$
• $y^2=41x^6+66x^5+156x^4+141x^3+48x^2+111x+59$
• $y^2=2x^6+82x^5+70x^4+6x^3+70x^2+82x+2$
• $y^2=140x^6+164x^5+68x^4+175x^3+50x^2+145x+89$
• $y^2=10x^6+16x^5+179x^4+58x^3+163x^2+146x+2$
• $y^2=112x^6+23x^5+47x^4+172x^3+47x^2+23x+112$
• $y^2=3x^6+100x^5+126x^4+159x^3+47x^2+95x+94$
• $y^2=154x^6+61x^5+44x^4+7x^3+96x^2+7x+51$
• $y^2=57x^6+91x^5+32x^4+16x^3+5x^2+137x+78$
• $y^2=3x^6+41x^5+172x^4+150x^3+11x^2+89x+117$
• $y^2=179x^6+166x^5+101x^4+102x^3+52x^2+100x+112$
• $y^2=37x^6+14x^5+154x^4+155x^3+145x^2+2x+126$
• $y^2=132x^6+108x^5+145x^4+103x^3+156x^2+140x+23$
• $y^2=101x^6+140x^5+149x^4+136x^3+149x^2+140x+101$
• $y^2=68x^6+23x^5+82x^4+98x^3+168x^2+174x+64$
• $y^2=4x^6+108x^5+20x^4+114x^3+74x^2+14x+29$
• $y^2=146x^6+70x^5+70x^4+176x^3+9x^2+120x+58$
• $y^2=17x^6+152x^5+158x^4+163x^3+158x^2+152x+17$
• $y^2=110x^6+24x^5+164x^4+156x^3+16x^2+84x+68$
• $y^2=157x^6+13x^5+26x^4+98x^3+104x^2+40x+85$
• $y^2=162x^6+55x^5+101x^4+110x^3+165x^2+162x+88$
• $y^2=151x^6+176x^5+120x^4+36x^3+7x^2+37x+22$
• $y^2=10x^6+7x^5+68x^4+10x^3+83x^2+76x+180$
• $y^2=119x^6+123x^5+118x^4+86x^3+70x^2+24x+90$
• $y^2=63x^6+176x^5+81x^4+125x^3+34x^2+179x+36$
• $y^2=108x^6+113x^5+37x^4+101x^3+37x^2+113x+108$
• $y^2=180x^6+88x^5+17x^4+123x^3+121x^2+35x+61$
• $y^2=17x^6+32x^5+162x^4+120x^3+162x^2+32x+17$
• $y^2=14x^6+66x^5+180x^4+62x^3+157x^2+140x+171$
• $y^2=13x^6+168x^5+80x^4+45x^3+108x^2+165x+94$
• $y^2=6x^6+49x^5+76x^4+75x^3+163x^2+60x+97$
• $y^2=130x^6+151x^5+149x^4+121x^3+38x^2+134x+23$
• $y^2=153x^6+168x^5+165x^4+135x^3+68x^2+168x+105$
• $y^2=175x^6+102x^5+64x^4+125x^3+168x^2+75x+35$
• $y^2=101x^6+107x^5+110x^4+107x^3+31x^2+89x+10$
• $y^2=32x^6+103x^5+74x^4+90x^3+173x^2+41x+163$
• $y^2=180x^6+152x^5+64x^4+55x^3+64x^2+152x+180$
• $y^2=24x^6+52x^5+110x^4+99x^3+28x^2+143x+129$
• $y^2=97x^6+93x^5+49x^4+13x^3+16x^2+129x+51$
• $y^2=25x^6+154x^5+158x^4+70x^3+31x^2+108x+1$
• $y^2=69x^6+78x^5+129x^4+37x^3+129x^2+78x+69$
• $y^2=23x^6+97x^5+62x^4+2x^3+12x^2+173x+51$
• $y^2=32x^6+26x^5+148x^4+145x^3+7x^2+46x+50$
• $y^2=10x^6+12x^5+141x^4+43x^3+144x^2+162x+9$

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.au 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.au : \(\Q(\sqrt{-1}) \).

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.ag_agc	$2$	(not in LMFDB)
2.181.g_agc	$2$	(not in LMFDB)
2.181.bu_bhy	$2$	(not in LMFDB)
2.181.an_io	$3$	(not in LMFDB)
2.181.ab_as	$3$	(not in LMFDB)