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

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

Invariants

Base field:	$\F_{181}$
Dimension:	$2$
L-polynomial:	$1 - 46 x + 878 x^{2} - 8326 x^{3} + 32761 x^{4}$
Frobenius angles:	$\pm0.0477114349732$, $\pm0.243779660740$
Angle rank:	$2$ (numerical)
Number field:	4.0.105456.1
Galois group:	$D_{4}$
Jacobians:	$48$

This isogeny class is simple and geometrically 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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$25268$	$1061559216$	$35155006789652$	$1151948707259440896$	$37738603808169621776948$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$136$	$32402$	$5928592$	$1073294350$	$194264280736$	$35161822336322$	$6364290751323928$	$1151936654923525534$	$208500535036022386072$	$37738596846852351342002$

Jacobians and polarizations

This isogeny class contains the Jacobians of 48 curves (of which all are hyperelliptic), and hence is principally polarizable:

• $y^2=140x^6+82x^5+16x^3+112x^2+60x+169$
• $y^2=14x^6+145x^5+67x^4+63x^3+112x^2+124x+23$
• $y^2=179x^6+127x^5+163x^4+120x^3+140x+30$
• $y^2=21x^6+115x^5+73x^4+177x^3+43x^2+81x+16$
• $y^2=40x^6+166x^5+52x^4+92x^3+123x^2+172x+109$
• $y^2=52x^6+71x^5+116x^4+78x^3+180x^2+30x+113$
• $y^2=32x^6+58x^5+147x^4+76x^3+128x^2+38x+153$
• $y^2=72x^6+119x^5+47x^4+22x^3+4x^2+72x$
• $y^2=30x^6+158x^5+103x^4+17x^3+46x^2+48x+100$
• $y^2=123x^6+103x^5+13x^4+71x^3+179x^2+153x+95$
• $y^2=101x^6+41x^5+172x^4+102x^3+142x^2+109$
• $y^2=69x^6+168x^5+96x^4+53x^3+87x^2+131x+132$
• $y^2=47x^6+8x^5+86x^4+93x^3+53x^2+17x+7$
• $y^2=74x^6+123x^5+117x^4+51x^3+110x^2+59x+145$
• $y^2=67x^6+80x^5+18x^4+71x^3+64x^2+110x+15$
• $y^2=57x^6+149x^5+24x^4+137x^3+43x^2+179x+49$
• $y^2=10x^6+14x^5+83x^4+39x^3+73x^2+13x+125$
• $y^2=83x^6+171x^5+168x^4+58x^3+71x^2+25x+150$
• $y^2=150x^6+4x^5+110x^4+163x^3+24x^2+15x+77$
• $y^2=73x^6+29x^5+161x^4+88x^3+142x^2+134x+4$
• and

• $y^2=8x^6+109x^5+167x^4+31x^3+122x^2+29x+160$
• $y^2=35x^6+95x^5+104x^4+82x^3+14x^2+148x+127$
• $y^2=139x^6+61x^5+119x^4+46x^3+155x^2+80x+78$
• $y^2=180x^6+170x^5+50x^4+58x^3+50x^2+169x+133$
• $y^2=123x^6+20x^5+2x^4+114x^3+40x^2+48x+4$
• $y^2=98x^6+160x^5+167x^4+91x^3+165x^2+18x+46$
• $y^2=15x^6+172x^5+87x^4+139x^3+144x^2+48x+11$
• $y^2=47x^6+122x^5+122x^4+140x^3+85x^2+52x+32$
• $y^2=91x^6+111x^5+114x^4+65x^3+18x^2+42x+52$
• $y^2=25x^6+38x^5+84x^4+145x^3+24x^2+161x+152$
• $y^2=68x^6+86x^5+178x^4+88x^3+33x^2+67x+162$
• $y^2=74x^6+114x^5+86x^4+26x^3+75x^2+72x+175$
• $y^2=101x^6+84x^5+123x^4+48x^3+101x^2+103x+163$
• $y^2=158x^5+144x^4+109x^3+161x^2+110x+155$
• $y^2=15x^6+2x^5+169x^4+146x^3+121x^2+6x+32$
• $y^2=140x^6+89x^5+13x^4+50x^3+101x^2+90x+54$
• $y^2=80x^6+120x^5+167x^4+29x^3+136x^2+132x+146$
• $y^2=161x^6+168x^5+27x^4+118x^3+138x^2+118x+17$
• $y^2=17x^6+39x^5+47x^4+158x^3+149x^2+2x+70$
• $y^2=175x^6+103x^5+137x^4+152x^3+179x^2+63x+5$
• $y^2=10x^6+150x^5+17x^4+9x^3+85x^2+19x+64$
• $y^2=138x^6+173x^5+29x^4+42x^3+92x^2+46x+91$
• $y^2=60x^6+100x^5+68x^4+84x^3+148x^2+37x+137$
• $y^2=139x^6+5x^5+42x^4+132x^3+22x^2+53x+94$
• $y^2=158x^6+167x^5+38x^4+131x^3+4x^2+9x+164$
• $y^2=103x^6+129x^5+141x^4+82x^3+57x^2+148x+57$
• $y^2=113x^6+176x^5+169x^4+56x^3+26x^2+174x+106$
• $y^2=58x^6+43x^5+154x^4+179x^3+150x^2+112x+96$

Decomposition and endomorphism algebra

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

Endomorphism algebra over $\F_{181}$

The endomorphism algebra of this simple isogeny class is 4.0.105456.1.

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.bu_bhu	$2$	(not in LMFDB)