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

• Label: 2.181.abv_biz
• 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:	$1 - 47 x + 909 x^{2} - 8507 x^{3} + 32761 x^{4}$
Frobenius angles:	$\pm0.0919956722480$, $\pm0.211005189210$
Angle rank:	$2$ (numerical)
Number field:	4.0.284445.1
Galois group:	$D_{4}$
Jacobians:	$24$

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$25117$	$1060565325$	$35154866511025$	$1151970369193277925$	$37738744066132427475712$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$135$	$32371$	$5928567$	$1073314531$	$194265002730$	$35161838208043$	$6364291008431715$	$1151936658077372131$	$208500535063377589947$	$37738596846966475988326$

Jacobians and polarizations

This isogeny class contains the Jacobians of 24 curves (of which all are hyperelliptic), and hence is principally polarizable:

• $y^2=125x^6+84x^5+137x^4+87x^3+139x^2+41x+139$
• $y^2=159x^6+93x^5+160x^4+127x^3+87x^2+125x+50$
• $y^2=130x^6+33x^5+26x^4+93x^3+122x^2+11x+174$
• $y^2=53x^6+173x^5+43x^4+106x^3+122x^2+105x+163$
• $y^2=4x^6+56x^5+125x^4+130x^3+109x^2+107x+32$
• $y^2=10x^6+175x^5+120x^4+38x^3+42x^2+117x+176$
• $y^2=51x^6+32x^5+141x^4+134x^3+99x^2+94x+134$
• $y^2=51x^6+134x^5+99x^4+125x^3+61x^2+33x+155$
• $y^2=122x^6+127x^5+119x^4+157x^3+153x^2+155x+51$
• $y^2=180x^6+124x^5+4x^4+69x^3+32x^2+83x+169$
• $y^2=23x^6+154x^5+25x^4+73x^3+42x+160$
• $y^2=143x^6+173x^5+70x^4+121x^3+124x^2+109x+141$
• $y^2=141x^6+114x^5+162x^4+11x^3+8x^2+9x+175$
• $y^2=97x^6+9x^5+178x^4+94x^3+94x^2+22x+19$
• $y^2=x^6+135x^5+112x^4+94x^3+170x^2+59x+48$
• $y^2=130x^6+x^5+27x^4+162x^3+92x^2+67x+173$
• $y^2=106x^6+157x^5+91x^4+148x^3+54x^2+178x+157$
• $y^2=154x^6+106x^5+180x^4+83x^3+91x^2+177x+154$
• $y^2=96x^6+27x^5+176x^4+121x^3+95x^2+90x+30$
• $y^2=163x^6+154x^5+6x^4+42x^3+168x^2+149x+93$
• $y^2=134x^6+64x^5+33x^4+163x^3+33x^2+84x+30$
• $y^2=18x^6+102x^5+2x^4+129x^3+35x^2+69x+151$
• $y^2=93x^6+166x^5+90x^4+179x^3+2x^2+32x+61$
• $y^2=164x^6+94x^5+103x^4+178x^3+61x^2+132x+104$

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 4.0.284445.1.

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_biz	$2$	(not in LMFDB)