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

• Label: 2.181.abv_biv
• Base field: $\F_{181}$
• Dimension: $2$
• $p$-rank: $1$
• Ordinary: no
• 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:	$1 - 47 x + 905 x^{2} - 8507 x^{3} + 32761 x^{4}$
Frobenius angles:	$\pm0.0525515266489$, $\pm0.225033026600$
Angle rank:	$2$ (numerical)
Number field:	4.0.8177037.2
Galois group:	$D_{4}$
Jacobians:	$12$

This isogeny class is simple and geometrically simple, primitive, not ordinary, and not supersingular. It is principally polarizable and contains a Jacobian.

Newton polygon

$p$-rank:	$1$
Slopes:	$[0, 1/2, 1/2, 1]$

Point counts

Point counts of the abelian variety

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$25113$	$1060295973$	$35151517455813$	$1151948008860622677$	$37738638883308874545408$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$135$	$32363$	$5928003$	$1073293699$	$194264461290$	$35161827203099$	$6364290825493239$	$1151936655554708995$	$208500535034815720779$	$37738596846712369116518$

Jacobians and polarizations

This isogeny class contains the Jacobians of 12 curves (of which all are hyperelliptic), and hence is principally polarizable:

• $y^2=158x^6+153x^5+61x^4+101x^3+86x^2+63x+104$
• $y^2=136x^6+62x^5+76x^4+126x^3+91x^2+120x+180$
• $y^2=92x^6+107x^5+54x^4+160x^3+121x^2+30x+7$
• $y^2=x^6+33x^5+162x^4+130x^3+23x^2+115x+161$
• $y^2=141x^6+117x^5+64x^4+81x^3+83x^2+71x+23$
• $y^2=149x^6+179x^5+130x^4+114x^3+37x^2+114x+68$
• $y^2=79x^6+106x^5+75x^4+73x^3+104x^2+139x+96$
• $y^2=140x^6+173x^5+122x^4+148x^3+5x^2+13x+82$
• $y^2=12x^6+77x^5+106x^4+170x^3+18x^2+65x$
• $y^2=111x^6+146x^5+148x^4+135x^3+59x^2+69x+72$
• $y^2=119x^6+86x^5+97x^3+120x^2+23x+82$
• $y^2=99x^6+161x^5+168x^4+20x^3+102x^2+155x+80$

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 4.0.8177037.2.

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_biv	$2$	(not in LMFDB)