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

• Label: 2.181.abv_bix
• 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:	$1 - 47 x + 907 x^{2} - 8507 x^{3} + 32761 x^{4}$
Frobenius angles:	$\pm0.0735271811030$, $\pm0.218603882480$
Angle rank:	$2$ (numerical)
Number field:	4.0.9288845.1
Galois group:	$D_{4}$
Jacobians:	$26$

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$25115$	$1060430645$	$35153191972535$	$1151959197600393125$	$37738691657319842226000$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$135$	$32367$	$5928285$	$1073304123$	$194264732950$	$35161832763327$	$6364290919433925$	$1151936656898553363$	$208500535051376627055$	$37738596846893397239302$

Jacobians and polarizations

This isogeny class contains the Jacobians of 26 curves (of which all are hyperelliptic), and hence is principally polarizable:

• $y^2=118x^6+150x^5+122x^4+156x^3+29x^2+74x+21$
• $y^2=106x^6+125x^5+4x^4+30x^3+166x^2+115x+18$
• $y^2=110x^6+77x^5+6x^4+161x^3+177x^2+90x+77$
• $y^2=3x^6+111x^5+158x^4+12x^3+170x^2+118x+154$
• $y^2=48x^6+143x^5+12x^4+103x^3+16x^2+42x+170$
• $y^2=55x^6+156x^5+63x^4+180x^3+52x^2+81x+71$
• $y^2=98x^6+9x^5+83x^4+150x^3+170x^2+52x+77$
• $y^2=116x^6+23x^5+164x^4+107x^3+114x^2+126x+153$
• $y^2=118x^6+177x^5+4x^4+179x^3+88x^2+34x+28$
• $y^2=30x^6+68x^5+17x^4+175x^3+90x^2+131x+45$
• $y^2=117x^6+24x^5+164x^4+126x^3+20x^2+147x+100$
• $y^2=175x^6+14x^5+32x^4+155x^3+12x^2+104x+61$
• $y^2=57x^6+60x^5+19x^4+122x^3+66x^2+92x+150$
• $y^2=96x^6+32x^5+133x^4+60x^3+28x^2+147x+170$
• $y^2=22x^6+77x^5+95x^4+100x^3+36x^2+43x+29$
• $y^2=38x^6+119x^5+31x^4+139x^3+148x^2+7x+158$
• $y^2=95x^6+20x^5+93x^4+172x^3+66x^2+42x+47$
• $y^2=24x^6+148x^5+110x^4+37x^3+157x^2+140x+91$
• $y^2=63x^6+122x^5+176x^4+75x^3+33x^2+46x+91$
• $y^2=124x^6+66x^5+137x^4+115x^3+83x^2+77x+130$
• $y^2=7x^6+165x^5+136x^4+152x^3+87x^2+139x+113$
• $y^2=111x^6+118x^5+25x^4+18x^3+50x^2+157x+115$
• $y^2=127x^6+50x^5+21x^4+79x^3+165x^2+132x+24$
• $y^2=99x^6+28x^5+148x^4+20x^3+99x^2+53x+22$
• $y^2=124x^6+156x^5+98x^4+96x^3+102x^2+6x+30$
• $y^2=44x^6+143x^5+164x^4+58x^3+124x^2+111x+164$

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 4.0.9288845.1.

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.bv_bix	$2$	(not in LMFDB)